What you want is called brazing, not soldering, and it will cause the silvering of the parts to be burned off so you'll have to re-silver it (assuming a silver plated trombone).
After reading this page, I think my answer is 'not much'!
Hmm. News to me - I've never heard this before. Got any references on that? Annecdotally I can only think of one person I vaguely know who liked playing keyboards. Again annecdotally one of my parents is a professional musician so you'd imagine some of that would run off and perhaps I'd be more likely than the average to be musically inclined having grown up in a house full of instruments and music, yet I have absolutely zero interest or inclination.
Sure people listen to music a lot, but never seen any other connection beyond that?
I'm currently working as a software engineer, but I made my living as a musician (jazz, blues, piano bar) for several years.
I could see jazz especially being interesting to tech folks. There's a fantastic mixture of theory and logic and puzzle-solving mixed with creativity and expression that meshes very well with hacker culture, at least to me. I personally know quite a few people who are into both.
It's also something that can be largely self-taught, which mean a lot of the people who are into it are into it because they're passionate about it.