

Jellyfin should work fine for what you’re looking for. I haven’t run it on a Pi but it should work on that. You’ll be able to play music using the web ui as well as mobile apps if that’s your thing. It can also transcode on the fly so if your current browser/device/whatever can’t play .flac directly it’ll automatically transcode the playback to .mp3 or whatever it needs to be.
There are some other self hosted music/streaming projects you could take a look at that are much more built out for music playback specifically. Look into Airsonic-Advanced or Navidrome for example - I’ve been meaning to check them out myself but haven’t gotten around to it yet.
I don’t think it’s possible, or at least not in the way you’re thinking. Encoding a video with lossless flags usually results in a file size bigger or about the same as the source, and on top of that it takes a long time to actually do the encode.
Video is already highly compressed.
But for sure you can tinker around with ffmpeg (FOSS) & see how it goes for you. I’ve done it in the past just for kicks since some of the common video codec encoders do have lossless flags but it really wasn’t worth the effort.
EDIT: That’s just the video in the file, you also have to contend with the audio. That’s a bit easier if you just want to use ffmpeg to dump everything into FLAC but again, I don’t think you’re saving much hard drive space if any.