HDMI and Audio
Surprising to hear of problems in this area.
I'm running a fairly ancient version of Mint (not at home, so I can't check, but probably 17.?). It has no trouble running two screens, one HDMI, one DP. And it plays HDMI audio (atrocious sound quality, but that's down to the crappy speakers in the screen). Switching to analogue output is simple enough, as the audio properties app is accessible via the volume control in the system tray.
A couple of years ago I had a sudden motherboard death in the middle of some important work. I shifted the system disk into a spare computer that was pretty dissimilar, and I don't recall any problems with video or audio.