This is a very big topic and I'll try to keep discussing it concise. So, let's first take a look at some of the most important sources for what we now call "Norse mythology", namely the Poetic Edda and the Prose Edda, and another important item, Saxo's Gesta Danorum.

It's unclear what the relationship was between the Poetic Edda and Prose Edda, and Saxo's Gesta Danorum. The production of the Eddas is generally dated to the 13th century, whereas Gesta Danorum was composed by Saxo around the 12th century. The Eddas are written are in Old Norse and Gesta Danorum was composed by Saxo in Latin.

The Poetic Edda, as its name implies, features numerous examples of what we today call eddic poems interspersed with a little prose here and there. Meanwhile, the Prose Edda contains quite a lot of prose and also many short items of poetry, including both excerpts of eddic poetry (several of them fragments of apparently longer poems) and many items of a type of complex poetry we now call skaldic poetry. Skaldic poetry was composed by a type of traditional poets, both male and female, known as skalds. These poets are often referenced by name, whereas no information is provided on authorship of eddic poems.

Both eddic and skaldic poetry are extensions of a particular type of poetry among speakers of ancient Germanic languages known by scholars today as alliterative verse. This is because it is heavily built around alliteration (the Old English poem Beowulf is well-known example).

Much about the Poetic Edda is enshrouded in mystery. It is clear than an individual or a group of individuals no doubt expended great time and effort to compile what appear to be almost entirely extremely 'pagan' poems. We do not know who did this or why they did it, and were these poems not compiled here, many would not have left a trace. This is all too common in the historic record (as an example, the philologically very important Old English Beowulf survives by way of a single damaged manuscript, just narrowly avoiding total absence from the historic record), and it would appear the eddic poems we have today represents a portion, probably a tiny portion, of what once circulated. We don't know who wrote them, why, and under what circumstances.

The author or compiler of at least some of what we call the Prose Edda today is generally held by scholars to be Snorri, an Icelandic skald and politician. This identification is complicated by a few factors, including the fact that we lack a manuscript from Snorri's time and because some Prose Edda manuscripts show significant differences, including notable additions.

Saxo's volumes are very different than the Eddas but it's clear that Saxo drew from at least some of the same material that can be found in the Poetic Edda and the Prose Edda—traditional eddic and skaldic poetry—and he states that he benefited from Icelandic informants. As a Dane, he would also have no doubt been familiar with contemporary Danish folklore, and probably also drew from that in some way. Additionally, Saxo injects a lot of Classical references throughout, which only occurs in a few places in the Prose Edda (like the Prose Edda Prologue).

Alright, with that out of the way, it's worth noting that the idea of Ullr as 'the most important god' is speculation. We don't have any concrete reason to believe this particular god was somehow 'more important' than some of the better attested gods, like Odin, Freyja, or Thor. The deity appears to have held a notable role of some sort, sure, and seems to have had a female counterpart (Ullin) but it's tough to say anything beyond listing what the record says and surveying reception of the deity (for a quick survey, check out Lindow's entry on him in his Norse Mythology: A Guide to Gods, Heroes, Rituals, and Beliefs).

As for Classical influence more generally, it's important to highlight that the Germanic languages, Hellenic languages, and Italic languages are all Indo-European languages, stemming from Proto-Indo-European, and speakers of Proto-Indo-European had a Proto-Indo-European culture, including a polytheistic belief system. Some perceived similarities you're discussing may stem from a common cultural heritage or may have been a result of some other means of diffusion, like early or late Roman influence, or they may not be as similar as one may initially think. It just depends on what you're referring to.

Finally, sources like Gesta Danorum and the Prose Edda Prologue all show some familiarity with Classical topics, but in the case of the Prose Edda Prologue, this influence is transparent and explicit, discussing topics like Troy and so forth. Eddic poetry does not mention Classical figures or concepts, and skaldic poetry generally also avoids any such discussion. In short, you're best off looking into specific matters on a case-by-case basis. You'll find a ton of modern scholarship surrounding almost anything in Norse myth, sometimes with widely diverging views. Lindow's aforementioned handbook is a great place to start exploring all these topics further.

Edit: Weird formatting