Im not from the states, so im not 100 percent sure on what your rules are etc.
But yes, You as a beatmaker does indeed get paid for live performances. You also get paid if your song is played on radio.
You just have to be registered at BMI/ASCAP. Am i wrong?
If an artist is interested in your beat and has a record label behind him/her then that usually also means that he or she has a budget. If the label sees this potential song as a potential hit and the artist really really wants it on his album, - then youre in a position where you can talk about prices. You're now able to demand a price for the beat.
But nope, this does'nt happen very often.
If you take this music thing seriously you should look for a music publisher or manager who can represent you and help you for example place the recorded songs (with the agreement of the artist/record label) in for example movies or commercials. There you also have opportunities for making money.
But it's a hard business of course.. Just like the "real" job market for all jobs available - there are also here in the music business limited amount of work.
Am i right or wrong? This is atleast the case in Scandinavia.