The mechanical license for a cover is non-negotiable and compulsory. Harry Fox will collect a set amount of royalty depending how many many copies you are planning to make. 100 copies will cost less than 1000, but you won't need to do any detailed record-keeping unless you go over your stated amount. My cover of Bill Withers "Ain't No Sunshine" cost me about $40, I think. I never burned anywhere near the number of CD's I'd planned to, but if i recall correctly, that was about the lowest amount. The same number of copies of a Led Zeppelin or a Lennon-McCartney song will cost exactly the same amount.
Streaming? Haven't a clue.
Sync license? I don't know if you can get one through HFA. Those are NOT-compulsory and the rates are NOT statutory. That means the publisher can either accept or decline your wishes, and charge as much as he/she wants.
Technically, you might need a sync license for a you-tube video, but the law and its enforcement is really FUBAR, so proceed with the same ignorance most of us have.
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If interested:
https://alonetone.com/tangmo/playlists/orphans-freaks/aint-no-sunshine-cover