1.   Do NOT advise on copyright unless you know the subject. Do not listen to advisers on the subject unless it is clear that they know.
2.   Copyright, and copyright rules, are jurisdictional. Different in the USA from England and different again in Australia and/or France.
3.   UK - MCPS
4.   USA, yes, there is a statutory royalty for re-recording, not sure of the current rules. ASCAP sounds likely but there used to be other agencies such as the Harry Fox Agency. Have a look on the ASCAP website. USA also permits parallel source licensing, so you can go direct to the composer or his music publisher, if you can find them, but a collecting society is likely to be easier.