Yep it's been said that when you die you respawn (a video shows a 4 or 5 second respawn time) with a bit of an armor penalty. and I'm guessing you just respawn at the nearest safe zone. Nothing has been said about you losing your armor when you die so I just assume you don't.
As for respawning in the capital, either in the hospital or in your apt. I would be fine either way.
and as for logging back on where you logged off, I don't think that would be a problem. And I hate to refrence WoW as I and many others have over and over
but it didn't seem to be a problem in that game at all. Lots of people logged on and off in that game and when they logged back on they were right where they left off. I don't think it ever caused any problems, definitely none that I'm aware of.
I wouldn't mind relogging in my apartment though, I just don't think it would be a problem to log in back to the place in the city where I logged off. Obviously that wouldn't work if you were on a battlefield because you could relog in the middle of a bunch of enemies, so they could just teleport you back to the capital or back to your apartment. Either way.