1) Unsurprisingly, sex is usually about power for her. She doesn't sleep with many people because a) she tends to channel her energies and frustrations into more violent or political pursuits, from which she derives just as much (if not more) pleasure, and b) she's acutely aware of how it could degrade her power base among her soldiers and her subjects. She sticks to people for whom she has at least SOME measure of trust, and who she knows want her more than she wants them.

2) Her first time, though, was a ruthlessly orchestrated seduction of the most attractive member of the palace guard. She learned as much as she could and then had him deployed to a remote outpost. (Though she is only aware of this on a very vague level, she chose him because he looked and acted the most like her father.)

3) She's not gay, but she tends to prefer women.