Not op but have a similar "problem". Straight up an earworm machine over here. But I can control it for the most part

Meditation is not my thing but if the song is getting annoying or too repetitive on a certain part I will intentionally try to distract myself. I certainly do have a monologue that reads, speaks, etc "out loud".

It only takes until i at least know a portion of the song enough to be able to sing along that I can play the majority of it ( as long as I don't get stuck in what I call a lyrical loop where one verse will tie back to an earlier one). It always sounds as is, with the band as well. Even if I don't know the lyrics I can hear the mumblings of that part.

1. Sure, but this just replaces the music with the sound of my breathing. There's always something in my brain. The only meditative peace I can get is in a flow state e.g. working out.
2. Yup, damn near always. Yak yak yak goes the brain.
3. Usually just vocals unless I focus on the music, or if it's instrumental then I hear everything.
4. Music that I can play in my brain on demand is usually music I listen to all the time already, with some exceptions. Don't have exact data on this, but it depends on context - if it's my favorite band then it'll stick around after 1 listen. If it's someone else or music I dislike it may take several listens.
5. I play The Axe by which I mean a ukulele. Not particularly well IMO but it's fun and relaxing.
6. I don't think so, but I can identify most songs I've heard before pretty quickly if I know the band or song name. It's like an involuntary Shazam.