Try Exodus at different times of the day. The new character locks are changed (I think) every hour. Early morning (EST) is often the best time to try.
End game is a bit of both. There is a duty finder that groups you with random players from any server in your data center, but you can enter pretty much anything as a full or partial group, too. (The exception is the large raids made up of multiple 8-man groups; you can't yet enter as a full alliance, only as individual 8-man parties.) There is also content that can only be done with people from your server (the current top-end 8-man raids), as well as open-world content that isn't instanced at all (fates and hunts). There's a party finder that lets people list specific content they're looking for members for, to help fill in spots for server-only content. You'll likely end up mixing and matching between running with friends/FC mates, randoms from your server, and randoms from the finder. And if you're into end game raiding, you'll likely end up with a static for the top end raids.
And yes, end game does involve grinding out tokens to fill in spots while you work on getting random drops. It's sort of like the WoW model. The best gear is random drops from the top raids, but there are a few kinds of tokens from various sources to round things out, and BiS gear is often a mish-mash.
Group sizes are 4 for dungeons, a few story mode primals (boss battles with no dungeon or trash leading up to it), and Wolve's Den (just kill 'em arena PvP), 8 for hard/extreme primals, a few storyline dungeons, and Coil (the top raid), 24 for Crystal/Syrcus Tower (3 8-man groups, duty finder easy mode raid) and Frontlines (24 vs 24 vs 24 objective-based PvP).
Currently, there is FC (guild) housing, and you can purchase a private room to set up within your FC house. There's going to be personal housing in the future at some point.