It is a courtesy and they technically do not have to do it but they will. Especially between UA/HA.

As for the rules/restrictions, IME that has always been based on the carrier to whom you give the bags. The carriers may work it out on the back end in terms of paying each other but I've never heard of folks paying fees to X for Y to carry bags, particularly for an interline partner in the States.

And all my "mod status" means is that I get to delete spam and settle fights in a couple fora; it certainly doesn't mean I know what I'm talking about.