Pretty sure Strawberry does everything you are looking for.
re: #1 I kind of had the same issue but with multiple music folders, most of the default music apps only let you use one folder. Strawberry lets you add as many music folders as you like, I’ve been happy with it.
On Windows I used to use foobar2000 which was great, and in theory I could get it running under Linux, but I’d rather just use something coded for Linux compatibility from the start.
There is an Linux compatible open source player being developed called fooyin (https://fooyin.org/) heavily inspired by foobar2000. When I tried it out a few months back it was still a bit rough for day-to-day use but it could eventually become a good alternative for people that miss the foobar2000 style player.