Basically, the server's in a really decent shape, i can confidently say this after being here since the beginning, the only downside is the low population for now, but it's still very playable, to be completely honest.
As to answer your questions:
1. I'd say almost all the activity happens in the End-Game.
2. All the level 90 Dungeons are Working, All the raids as well, LFR, Normal and Heroic, Also Challenge Mode: Gold is obtainable, they still are getting fine-tuned at the moment but still playable. You can check the progress here:
List of all Available Dungeons & Raids <Updated>.
3. PvP is getting some work, Pathfinding is being implemented in a ghostly manner but still there, fixes happen quite often if well reported, you may check the latest changelog here:
September 28, 2017.
4. And to your very convenience, The Conquest Catch-Up Mechanic was implemented at the start of this PvP Season, which makes it fairly easy to catch up with the old and well-settled players currently playing.