1 - Why does the qr// operator accept the /o midifier?
Just for compatibility reasons, it doesn't actually have any effect on the resulting regex object.
2- If you combine one or more parts defined with qr// in a regex with some non-precompiled stuff, do you still get the advantage of precompilation?
In your example, you get the advantage of compilation with the regex objects but the match still has to be compiled dynamically since it contains variables (although with regex objects should be slightly faster than plain strings since they're already compiled).
3 - If there was a non-compiled var reference in the above m//, do I still get any benefit from pre-compiling the other parts?
Yup, as the regex is already compiled, where as a plain string has to be compiled first before matching.
4 - What happens if I add a /o modifier to the m// above?
I believe the effect would be the same if you were using plain strings as it would compile to the same thing, so the result would be that match regex would only be compiled once and once compiled it's always the same. So you'll get a tiny benefit with the pre-compiled regexes on first compilation, but in the long run it's pretty negligble.
5 - If one or more of the per-compiled parts (and/or the non-precompiled parts) contains capture brackets, was there any benefit (in performance terms) from pre-compiling some parts?
There's no reason for capturing to effect the performance of a compiled regex vs a compile'n'do regex, as once compiled a regex will perform the same whether it was compiled or otherwise.