You aren't going to like this but: it depends

If you want to be perfectly grammatically correct, you should listen to your spell checker, and also get some other advice (spell-checkers often get things wrong). On the other hand...
There's a bit of subjectivity. Personally, I don't mind lists as fragments, but I get rather annoyed by other types of fragments. The general rule I would use is, does the sentence or fragment confuse the reader? I don't think your lists do. But this site gives some examples of fragments that grate:
http://owl.english.purdue.edu/handouts/grammar/g_frag.htmlIn casual discourse (eg, responses on an internet message board), I relax my grammar guard. One could argue that some types of novel are also intended to be more relaxed than formal. I think the bottom line is, is your style easy for your reader, and does it convey your ideas? After that, I might be concerned if certain grammatical errors made me look like an ignoramus, and might pick and choose from there.
You might like to get a slim volume on grammar, such as "Elements of Style":
http://www.bartleby.com/141/