I have a few questions...
No kidding, haha. I'll take the challenge
Is it even possible to get a character to 335 without doing the raid
Yes
and if so are you limiting yourself in how fast you can get there?
This is ambiguous, sort of yes, but also kind of moot. How
fast you get to 335 is almost completely irrelevant in my opinion, since there's absolutely zero reason to
be 335. In my opinion there's more fun to be had in seeking out the most appealing gear you want and then raising it up as infusion material comes to you. But the raid (particularly challenge mode) is of course a good source of said infusion material.
Without doing the raid what are the best options besides the Nightfall to move up LL wise?
Challenge of the Elders is very rewarding all around.
Ranking up any faction, including and especially Variks (which you can do via rep gains from CoE as well as original PoE/Skolas) gives light-progression gear. Gunsmith too.
Farming any kind of named Ultra bosses with Three of Coins for exotic engrams is also viable progress.
The unique strike reward gear (i.e. Flayers cloak, Grasp of Malok, etc) can drop at high light.
Trials of Osiris and Iron Banner.
What is the CoE all about? Just a bunch of boss fights?
Three rounds, each with a boss, with modifiers plus an additional score multiplier for certain actions, all changing on the weekly reset. This week the bonus points are for grenade kills. You can get a sigil from Variks for guaranteed rewards, once per character per week.
What kind of rewards do you get?
Queen's Weapons and House of Judgment armor and class items, the House of Wolves exotic weapons at high light, ghosts, glimmer, House of Judgment rep
Has the regular PoE with Skolas been updated to give out 320+ LL rewards?
The rewards for completing PoE have not been changed, however this is also to say that you still gain just as much rep for completing them, and the House of Judgment rank-up rewards have been updated.
What range of rewards do you get for CoO now?
Court of Oryx will get you high-level artifacts and seemingly a high chance of dropping the playstation exclusive armor engrams.