I figured out they had been lovers during the very first scene she appeared in. As for what I think about their relationship? It's just another example of Trek--a more militaristic one, no less--disregarding the real-world issue of fraternization. It makes for easy drama, but still annoys me to no end.
There's no reason that because modern militaries in some nations wouldn't agree to something, Starfleet wouldn't either. From what we see, Starfleet officers spend most of their lives out in space on starships surrounded by, mostly, other officers. To prevent fraternisation would essentially mean that joining Starfleet would make you semi-celibate for most of your life. The realities of long term deep space missions probably make it impossible to enforce such rules and probably undesirable.
Her career was still ship's counselor, she just had authorization to command a bridge watch, and even then in the even of anything serious, she'd turn command over to Picard or Riker. Were she ever to advance up to Admiral, she would not be in a position where she'd ordering Sisko how to deploy the fleet or where to take the Defiant during the Dominion War.
Spock presumably had command training, and indeed wore a command uniform in WNMHGB despite his post being science officer, Scotty never had his own ship, and Crusher basically commanded a flying hospital.
Not everyone at the Academy takes the Kobayashi Maru. Spock didn't. Attending the Academy does not automatically qualify you for command, otherwise she wouldn't have had to take that test in Thine Own Self.
