A1: I think most people are more comfortable to known characters, myself included. The problem being, too many fan-fics do not capture the true nature of said characters. Indeed, many authors have an agenda (both good and bad) they want to present, and the end up "destroying" the essence of our beloved characters. So, for me personally, I don't mind meeting new characters.
A2: As long as it's not a cross-over story, great. Don't "borrow" Gibbs from NCIS or Grissom from CSI. And by all means, leave H. Caine in Miami. Make up new characters, with their own personality. Don't write CSI / NCIS characters with a different name. But, yes, expanding the Trek world beyond Starfleet is always welcome.
A3: No idea, sorry.
A4: This is a PG board. Or at least PG-13. So, I'm not in favor of sex scenes. Hinted at or mentioned discreetly, sure. Graphic detailed sex scenes, please don't. Ditto for violence. Acknowledge that it happens. Again, there's no need to get into graphic detail during a hand-to-hand fight scene. Just give the readers enough to know what's going on, and let their imaginations take over. Lovecraft is weird? No, Lovecraft is horror. Personally, I'm not big on horror.