continue with your class quest if you have not finished it. Do Dailies (repeatable quests) on Belsavis and Ilum.
Do Hardmodes (normal Flashpoints only harder) with peoples and hope better gear drops for you.
Best thing to do is find a Guild on your server and get to know a few people that you can group up with etc
The character select screen is stuck in that view i believe.
The cover mechanic is only a game play element that is used by Agents and Smugglers. Your Bounty hunter gets no benefit from it. unless your using Line of Sight to stay alive behind a BIG crate
There is still chances you could come across the Republic while questing on NS, if you are both flagged have at it. But only outside of the central hub as stated above
For empire its in the 32 - 36 range. Note : their is no Republic zones on the planet for empire players either. if you want impromte PvP then get to Nar Shaddaa since that's when both factions start meeting.
Just because he has done it that day (Heroic quests have 24hr cooldown) does not mean he can't join your group and help you do it. It just means he can't complete the quest itself again yet
Class quests are not repeatable and your friends do not impact those decisions anyway. the only repeatable quests that i am aware of are flashpoints or dungeons/instances that require a group. these are repeatable. ie Black Talon or Essele (SP?)
1) surnames are part of the legacy system, not sure myself on how you access that.
2) you can't have a biography that i am aware of, some else may be able to state otherwise but i don't think you can