Who owns a copyright?

I wrote a song and found a "part-time" producer. He's been playing music in my area for several decades, and his hobby is helping musicians get some of their music professionally recorded. Since he was friends with the studio owner/engineer, he paid a discount rate. He also paid some of his musician friends to sit in on the recording. This was all on the verbal agreement that he would be entitled to a portion of the profits from this song, assuming there would ever be any. I didn't pay anything to have the song recorded.

I know I own the copyright to the song itself, but does the producer own the copyright to the recording? Since he paid all the other parties, he would be the only one entitled to the rights to that particular recording of my song, as everyone else was "for hire." But I haven't found anything in copyright law that refers to a recording. Only the song itself.

Also, what if I wanted to take the recording to another studio and pay musicians to duplicate the parts of the song that his musician friends played? Would that be allowed, or are those parts copyrighted?

I received a copy of the recording. Am I at risk for copyright infringement if I publish the song online, even if I'm making no money from it? I would assume that even if it went to legal action, he'd be hard pressed to prove it since there was no contract involved. But I want to do the right thing, not just what I can get away with.