Toptal is cool. They do their best to make you feel that you are part of a team and not an individual contractor and I would say I didn't expect this much from their side. The support I receive is top quality. Will recommend it if you are okay with them taking a cut over your income and following their terms and conditions.
I use headphones mainly for noise cancellation so therefore my vote goes to Bose QC 35 II. Additionally, I use it as ear cover if co-working AC gets too cold.
You can search Angellist for remote and internships I think.
I'm not sure about a site dedicated to this, but as @aviaryan mentioned you can search on regular job boards and use the right filters.
Having said that, I would advise against doing a remote internship. The beauty of an internship is that you get a chance to work with more experienced people and see what it's like to work at a company. I think by doing this remotely you lose out on much of that.