1. Technically, yes. Open up the console by hitting the Tilde (~) key or whatever your equivalent is for international keyboards. With the console open, click on Karna with your mouse and you'll get an ID that pops up in the middle of the screen. Write this down somewhere because you'll need to use it again later.
With her selected, now enter disable and you can keep playing as normal. Whenever you want to use her again, open up the console, enter prid followed by the ID you wrote down earlier. Hit Enter, this will select her reference.
Then just enable and moveto player then she'll be back.
2. Yes. It's exclusive to female players, but there's a mod by TheShiningAbsol that makes it possible to romance her as a man.
3. For romance? No. You can safely dismiss Bacchus, I don't remember where he goes to, but you also have the Summon spell to bring him back.