1) How many quests can you have at once?

2) can you drop quests and return to them later?

3) Can you do quests of enemy factions?

1. Not sure. Never hit the limit... I'm pretty sure quite a few, if there's a limit at all.
2. Yes. Dropping a quest will force you to restart the quest chain over, though, so be mindful of what you're dropping.
3. Only after level 50 as endgame content.