I'm not 100% about the audio issues. Analog audio out of the RPi isn't great so almost no one uses it. Some time ago audio quality was improved via a firmware update (see this thread here Analogue audio testing - Raspberry Pi Forums) but this seems to have caused higher GPU load and people reported issues with HEVC playback or deinterlacing.
Going the HDMI route isn't easy, if you use HDMI then the analog video output will be disabled.
Probably the easiest and cheapest method will be to use one of the plenty RPi soundcards. Hifiberry, Iqaudio, Justboom, Pimoroni pHAT DAC and several others work out of the box (some need a dtoverlay line added to config.txt) or if you want it cheap get some RPi soundcard with a PCM5122 or PCM5102 from Asia - they should work fine as well and provide a lot better audio quality than the on-board output.
so long,
Hias