For romance, you can go to your camp and chat with your teammate after each quest or event; you can go in and out without sleeping for your roleplay.
By being friendly and doing your captain duty, some of them will think you want to start a romance ^^!
I play in tactician mode, and the only "timer" I can think of was in the underdark at the end of Act 1 when you have to save a true soul and Wulbren.
In Act 3, there is only one quest that will require you to do it without sleeping, pretty obvious when you get it.
Without spoilers, and in order to help you get some rest, it is in lower town.
There is also a turn-limited quest, but you are safe as long as you don't go to a particular place.
