TT is very snowbally, probably 2x more than Summoner's Rift. Even 1 early kill can snowball into an early victory, depending on who you're playing.
Towers should always be prioritized over alters if you have time to choose between them. Altars are a win-more objective, just like Vilemaw. Always try to keep at least one on in your control though, because that buff is pretty strong.
Any of the 3 roles can carry on Twisted Treeline. It all depends on what you play best.
Bruisers (Darius/Illaoi/Olaf), tanks (Poppy/Maokai/Zac), and fighters (like Vi/Riven/Yasuo) tend to carry the hardest on TT.
Marksman has always been the weakest role on TT, but even more so with this new season. Graves and Caitlyn are probably the best marksmen on this map. The former because he's pretty much a ranged bruiser, and the latter due to her safety and utility. In general, marksmen have a very slim margin for error compared to the other classes. If you get behind as a marksman, it is very difficult to come back into the game, and sometimes you don't even have to make a mistake to get snowballed on.