Are you converting flac to flac though? Flac is natively gapless. If you are doing flac-to-flac, that's really strange. I've done 100s of opera recordings, many of which don't have gaps between tracks and have never had this problem.
Maybe you don't have "Use gapless for sequential album tracks" checked under Options-->Audio-->Track Change?
Regarding tagging, what's output, I believe, is going to be reflected from what was on the original cue sheets; so you're likely going to have to re-tag the files if you go this route. You can try highlighting the album, right clicking, and select Library Tools-->Lookup track info from online database. MC's metadata sources are not robust, however (which is one reason why the program doesn't cost as much as Roon, say).
You can also cut off all the irrelevant stuff before "01 - Burning Times," say, but you'll have to dig into the expression language (search the wiki) to do so. Someone on here might be able to help you with that better than I, for though I can do it, I'm not that proficient.
A couple of other options for retagging: try an external program like MP3Tag or dbPoweramp and then "Update Library from tags" in MC; or try MCUtils, which allows you to tag from AllMusic, Musicbrainz, and/or Discogs. The latter does take some setting up and has a learning curve. Search the forum for MCUtils, and you'll find some posts linking to it.
Edit: Wer's right: I misread what you posted and thought you meant tags, not file names. Sorry for the misunderstanding!