Other than the planet differences (PvE, PvX, PvP and economy) are there any distinctions between the races? For example Demons are stronger by nature therefore better tanks/ fighters, Beastmen are faster and more agile therefore better archers and Humans are a balance between then 2?
The race spotlight has some of the differences between races, and the character creation spotlight shows the differences in possible attribute distribution when creating a character of different races.
Does the God you pray to matter (for example Elysium is part of the Greek mythology)? Do you get any kind of buffs or debuffs in the game at any given moment because of your religion?
You can pray to the god you worship for blessings and divine quests to alter your karma, but there hasn't been a lot of information about the gameplay effects of the religion system. There was mention that Babilis will put a beacon on worshipers of Talos if they stay on Tartaros too long, so it's assumed that the choice of which god you worship will be fairly significant.
Are all races given the same chance to acquire knowledge? From what I have seen Beastmen will have access to more plants, meaning botanology and other professions like that will be easier for them to learn that the Demons that will be more hunt-focused to get the fure, bones and so on.
Every race can acquire all knowledge (except for maybe demons for good only areas of Arboreus), but, as you point out, availability will differ for each race. For example, it's going to be much harder for good aligned beastmen to gain knowledge of certain parts of Tartaros than it would be for a demon, but it's still possible.