The English language is still not very standardised, for what it's worth. Instead of standards what you're seeing is simply conventions. Spelling still varies considerably from country to country, and even within a single country there is variability both regionally and on a person-to-person level, like how I've just spelled standardised, for example, despite having an American education. There is no official standard of English in America, for example. While most dictionaries for Americans will agree, this consensus is a matter of convention and not the result of any sort of national government oversight.

• did the idea of a wrong spelling exist?

Not really, no. Variant spelling was the norm, not the exception. Related to that is the answer to another of your questions:

• Did people get upset at a wrong spelling or usage of There/Their/They're?

Also no, this would not be a usual thing. As an example, about a month ago, someone asked a similar question regarding the spelling of "show" as it was once "shew". Like many "wrong" spellings, it's actually an earlier spelling of a variant pronunciation. You find it in Shakespeare…

Come, come, throu boy-queller, shew thy face (Troilus and Cressida)

…but also in more recently for example in HP Lovecraft's writings. This spelling was still very much in use in writing well into the 20th century. In the 1920s while it was less common than you'd find in the 1820s, it was still in use. At this time it coexisted with the "show" spelling, as well.

The notion of what's "correct" spelling is largely the result of various language/spelling reforms which have happened throughout the history of English and many other languages as well. Usually these take the form of dictionaries, which are themselves generally tied to individual dialects. In Australia the Macquarie Dictionary is often considered the standard of Australian English spelling and usage, though like all dictionaries it's describing use and not telling people how things should be. Webster's has long been considered an ideal for American spelling and usage. Canada has the the Canadian Oxford Dictionary. These three dictionaries will not agree on a large number of spellings.

Likewise in each of these countries there have been proposals for spelling reform, but these are only as good as how much people are willing to adopt and conform to them. In Australia this was met with some success in the 1970s, and Macquarie is reflective of this. Some efforts were less successful, such as America's proposed simplified spelling which was backed by President Roosevelt and Andrew Carnegie. Noah Webster's efforts were a little more successful and were propagated through his dictionary. Someone else might be able to speak more on specific efforts in Canada which I'm not as aware of.

Spelling reform is a pretty major issue in most large languages, and efforts have been made for centuries to create a more uniform standard within a given variety (or country), but not on a larger "all of English" scale. What this means is that if you take a point in the past couple hundred years up to today, the different standardisations you're seeing are actually pushing the different varieties' spelling systems further apart. What conventions there are that might shared between varieties of English are themselves often just the luck of the draw, being the chosen spelling out of a variety of possible spellings that were once in use. You can see this if you look at older texts, where a single word might be spelled two different ways even in a single paragraph, and definitely different between two different authors.

If there are future spelling reforms in American English, it will be done to represent the American pronunciation more phonemically, and not take into account the way words are pronounced in other Englishes. This means that over time, if the trend continues, you could potentially see a split where someone in the US could actually have trouble reading something written in England. We're obviously not there, but it's not impossible.

Anyway, since language standardisation is primarily a function of the educational systems, which usually follow national borders, you're going to see less standardisation on a global scale over time, not more.

• Are there any Latin texts of someone criticizing another writer for using the wrong case endings, etc?

This should not be confused with spelling. There are different categories of grammar "mistakes". There are a bunch that are "real" and which a native speaker would never mess up. These are the ones learned basically in childhood. Then there are a bunch of others which native speakers do mess up but which they would also concede as being "wrong" if it was pointed out. Things like saying "ain't" (which is actually not only common and acceptable in many dialects but is also the historically correct contraction of "am not") are in this second category. It's this smaller category that the grammar nazis are picking at, because the actual rules that no native speaker messes up (e.g. certain contractions in sentence-final position) simply never come up, because again, no native speaker messes these up.

The reason I bring this up is to say that the case endings issue is really one of those mistakes in the first category where you're not going to see it happening among native speakers unless they're little kids, and even then little kids only tend to mess up the irregular few that exist, and they mess them up by saying them as if they were regular (e.g. "runned" instead of "ran").

I work mostly in Sinotibetan languages, as the flair states. That means looking at a lot of stuff written in Chinese characters. What you find consistently is a similar degree of variability in old texts. For example what's now standard as 面 might be written 靣 sometimes. In these earlier texts this is often not a mistake though. Instead it's treated as stylistic, such that you might see a single page from a single text with both of those writings in use. The person doing the writing might simply be looking to add some diversity to the text to make it look "better". You'll often see both 爲 and 為 or both 匯 and 滙. Those pairs are the same word, just with the components rearranged slightly. And whether they write 厅 or 庁 (China for the first, Taiwan/Japan for the second) won't make too much of a difference in readability, especially if (like "shew" and "show") you've grown up seeing both.

So then back to the question:

• Are there any Latin texts of someone criticizing another writer for using the wrong case endings, etc?

Generally we don't see this happening, no. There are things that are expected to follow a certain style, such as certain styles of poetic rhyme and meter, and so you'll find people writing about that or what it is, but often well after the period in which that was followed. We don't really have much in terms of texts telling people to stop saying "aks" (which by the way, like "shew", is also historically a variant pronunciation which has been in use for the same amount of time as "ask" has in the history of English. That people decided "ask" should be the so-called standard is 100% by chance, and it could have just as easily and correctly gone the other way).

Hope that helps. Sorry it got long. Let me know if you have any follow up questions.