I will answer the first part of your question. (and I humbly request someone who knows better than me to give a full comprehensive one)
Jacob Ludwig Carl and Wilhelm Carl Grimm (known better as the Brothers Grimm) compiled a huge array of folk tales from various sources in an effort to preserve Germany's cultural heritage and promote solidarity amidst a Napoleon-dominated Europe. Primarily gathered from Hessian and Westphalian soil, they compiled these stories from numerous sources, primarily from the lips of people from lower classes (although oftentimes upper class people also chimed in). So it is safe to say that these tales were fairly well known before the famous publishing by the Grimm brothers, although they definitely were not part of widespread literary discourse during that time.
They werent strictly "fairy tales" in the sense we know them today, and the brothers Grimm actually didnt use the term for them. These stories were folklore, legends, mythology, passed down as oral tradition for centuries. These stories often contained mature and violent themes in them and touch on some very sensitive (or as we put it, NSFW) subjects.
Now were there changes? Yes.
In 1810, they sent Clemens Brentano, a poet and writer, these tales. However Brentano didnt like these tales, somehow, and left his copy in the Olenberg Monastery where it was eventually lost. Somehow by chance it was rediscovered in 1920.
When comparing this copy (known as the Olenberg Manuscript) to the official editions of the Grimm's tales in 1812 and 1815, some differences begin to emerge. Much of it was due to the fact that it was difficult for the Brothers Grimm to faithfully copy down the exact words of the tales they heard. Another reason is that they themselves made some intentional changes to the story. They felt it was justified because they felt they understood the natural "poetics" of storytelling. Oral tradition always has a habit of mutating over the centuries and they felt as long as they could capture the "gist" and "essence" and "moral" they were doing the story justice.
Not all the stories were strictly German (some were of French and Dutch origin but found a popular audience among Germans), and some had actually been published in older more obscure books. (The Brave Little Tailor was from a 1557 manuscript)
("Sleeping Beauty" and "The Little Red Riding Hood" were also originally actually published by Charles Perrault for example, and had some prior following. )
Jacob Grimm sought to establish a more "Germanic" form of storytelling. Rather than fey, they became enchantresses. When there were glaring plot holes in the story he sought to fill the gaps with his own effort.
Willhelm Grimm sought to cater to a more "popular" audience. Evil mothers became evil stepmothers (like in Snow White). He also used more "literary" words to give the story style and attractiveness. It is very notable though, that they didnt tone down the violence in many of these tales...
Overall I can say this: it was a good effort of them to copy down and preserve these wide collection of tales that would have eventually faded into obscurity. Some changes were made, out of necessity or otherwise, but overall the core tone of the stories was preserved. It is also important to note that many of these stories were not originally intended for children, and was later bowdlerized again to make it family friendly.
Thanks to /u/integral_grail for a solid answer! I can give a more comprehensive answer, but you definitely laid out some of the basics.
So: "Where the tales collected by the Brothers Grimm widely known before they compiled them?"
Yes, they were (or at least, the vast majority of them were). We have records of tale variants of most of the tales the Brothers Grimm collected from all over the world, sometimes several variants from a single location, from different centuries. Cinderella, for example, has over 500 variants in Europe alone! Many of the tales the Brothers Grimm collected were widely known and circulated in various forms for hundreds of years before the Grimms came along. The brothers themselves were heavily influenced by the French versions of several of their tales, for example. Several of the more popular versions of well-known tales (the versions of Cinderella, Red Riding Hood, etc that we think of today when we say "the story of [x]") were actually first widely circulated in Italy, France, and Spain before they ever reached Germany on the same level.
This actually leads into your second question, "Did the more popular ones (Snow White, Cinderella, Red Riding Hood) match the ones more popular before they collected them?" The short answer is "no." The slightly longer answer is "many bore a lot of similarities, but every variant is different."
Maria Tatar actually briefly covers this in her introduction to The Classic Fairy Tales:
Fairy tales, Angela Carter tells us, are not "unique one-offs," and their narrators are neither "original" nor "godlike" nor "inspired." To the contrary, these stories circulate in multiple versions, reconfigured by each telling to form kaleidoscopic variations with distinctly different effects. When we say the word "Cinderella," we are referring not to a single text but to an entire array of stories with a persecuted heroine who may respond to her situation with defiance, cunning, ingenuity, self-pity, anguish, or grief. She will be called Yeh-hsien in China, Cendrillon in Italy, Aschenputtel in Germany, and Catskin in England. Her sisters may be named One-Eye and Three-Eyes, Anastasia and Drizella, or she may have just one sister named Haloek. Her tasks range from tending cows to sorting peas to fetching embers for a fire.
......The story of Little Red Riding Hood, for example, can be discovered the world over, yet it varies radically in texture and flavor from one culture to the next. Even in a single culture, that texture or flavor may be different enough that a listener will impatiently interrupt the telling to insist "that's not the way I heard it." In France, Little Red Riding Hood and her grandmother are devoured by the wolf. The Grimms' version, by contrast, stages a rescue scene in which a hunter intervenes to liberate Red Riding Hood and her grandmother from the belly of the wolf. Caterinella, an Italian Red Riding Hood, is invited to dine on the teeth and ears of her grandmother by a masquerading wolf. A Chinese "Goldflower" manages to slay the beast who wants to devour her by throwing a spear in his mouth. Local color often affects the premise of a tale. In Italy, the challenge facing one heroine is not spinning straw into gold but downing seven plates of lasagna.
The French Cinderella by Perrault, for example, is the version with glass slippers, a fairy godmother, and a pumpkin carriage. The Brothers Grimm version? Her "fairy godmother" is the spirit of her dead mother who resides in a tree, there is no pumpkin carriage, and she is gifted three beautiful dresses (one for each night of the ball) rather than a pair of glass slippers. Basically: every version of a tale is different, especially ones based in the oral storytelling tradition. Location, class, time, and the teller all affect how the story is told and what story is told. This is why fairy tale scholars usually examine the underlying basic plot structure (known as a "tale type") that appears despite rich cultural variation rather than trying to find exact copies of tales transmitted across cultures. When we do find tale variants that are remarkably similar to each other in plot, theme, tone, narrative structure, and language, that tends to be a sign that those two cultures were communicating with each other on a fairly regular and intimate basis via trade, immigration, or other forms of cultural exchange.
Your third question, "Were they immediately of academic interest?" is a little bit tricky, because the Brothers Grimm themselves were trying to collect, preserve, edit, and distribute the tales due to their academic interest in them; their initial collection of the tales was what essentially amounted to a literary archeological expedition (complete with making it up as they went along). As they stated in the preface to the 1812 edition:
“It was perhaps just the right time to record these tales since those people who should be preserving them are becoming more and more scarce...Wherever the tales still exist, they continue to live in such a way that nobody ponders whether they are good or bad, poetic or crude. People know them and love them because they have simply absorbed them in a habitual way. And they take pleasure in them without having any reason. This is exactly why the custom of storytelling is so marvelous.”
I think I would need further clarification on whether you were referring to the Grimms' collection 'Kinder-und Hausmärchen/Children's and Household Tales' or whether you mean fairy tales more generally. I've previously detailed here and here how the Brothers Grimm were extremely self-aware that they were preserving German heritage and how many of the fairy tale collection collectors/editors did so due to the rise of romantic nationalism and the rise of a "scholarly interest" in folklore and fairy tales/wonder tales. In general, academic interest in wonder tales/household tales/fairy tales has been around since at least the late 1600s/early 1700s with the rise of French salon culture and the renewed interest in such tales among the aristocracy, though serious academic interest didn't arise until the late 1700s/early 1800s.
Parsing out whether the Grimms collection was of immediate academic interest is a little more...convoluted because they weren't working in a vacuum; as I stated before, they were operating within the rise of romantic nationalism and a rising academic interest in folklore and fairy tale collection and dissemination. They were themselves scholars employed at the University of Göttingen as professors and librarians and later at the University of Berlin. It's important to stress they produced other things besides their collection of Household Tales, though that is what they are most known for today: Jacob's collection Deutsche Mythologie (German Mythology) in 1835 was actually considered a more valuable addition to the German literary landscape at the time than the Household Tales (then in their third edition), and they were working on a comprehensive German dictionary at the time of their death. They also compiled collections of folk music and literature, and Jacob did a lot of work in the historical linguistics field. You can view a more-or-less complete list of their works here. In this respect, both brothers were quite prolific in their scholarly outputs, and their efforts did not go unnoticed.
As folklore and fairy tale/'wonder tale' collection and dissemination became the focus of scholarly attention throughout the 1800s, the Brothers Grimm worked in scholarly concert with a growing number of other fairy tale collectors and scholars: Joseph Jacobs and Andrew Lang in the UK/Scotland (as well as John Campbell), Asbjornsen and Moe in Norway, Alexander Afanasyev in Russia, and later, Antti Aarne and Stith Thompson (who pioneered the Aarne-Thompson organization/categorization method to categorize tales by "tale types"), along with many others. Various folklore societies and journals were founded throughout the late 1800s as the field grew; Georges mentions that "For literate, urban intellectuals and students of folklore the folk was someone else and the past was recognized as being something truly different." All were working generally for the same reasons: to collect, preserve, study, and disseminate folklore for scholarly reasons (though said specific reasons varied). In this respect, all fairy tale collections were of academic interest, because they were all being collected and published for largely scholarly reasons. However, if you're asking whether or not the Grimm collection was of a particular academic interest or whether it was unique at the time of the first edition's publication, the answer is "no." The Brothers Grimm had much more luck marketing their collection towards the rising literate general public than they did the academic world at the time of publication (even though the collection was originally compiled for academia). The academic interest in various specific collections of tales wouldn't really happen until the early 1900s.
For more information, I would consult the following sources: