Q1: Yes to all that. You have all kinds of fans who like all kinds of fan fiction. Some prefer canon characters while others like original characters. Also some like certain eras, like TOS or TNG, while others are open to reading stuff from every Trek era, even ones not shown on TV or film. For my own fan fic, I use a combination of canon and original characters, but more original characters. I use the canon characters more to set my stories in a certain time frame and to add a certain flavor to my stories. Plus part of the fun is having my original characters interact with some of the characters I grew up watching on TV.
Q2: Yes again. It's a subjective thing, but I do think there is an audience for all kinds of Trek. I wouldn't worry so much about what people like at this point. Just focus on the kinds of stories that interest you and that you want to invest the time in researching and writing. I think you'll enjoy it more and readers will too.
Q3: I got my feet wet reading fan fic from this website, also Trek Writer's Guild, Fanfiction.net, and various websites. Ad Astra is another place where fan fiction is posted. Some of my fellow United Trek writers post there as well. One good place to check out is the Star Trek Expanded Universe Database. It can provide a good overview for a lot of fanon out there. As for canon information, back in the day I bought a Star Trek Encyclopedia. But now there's the very useful Memory Alpha website which mainly deals with canon stuff. The Memory Beta website deals with canon stuff, but also includes information on novels, comics, video games, etc. Both of them are great resources.
Q4: This forum is PG-13 so I don't know if that's the level you want to write. You would have to surf some of the fan fiction sites to see their various ratings levels.
As for your ideas, I skimmed them. From what I read I thought they were good ideas. I recommend just diving in and writing any of them, or all of them.