Pro-am here is always separate from the amateur events.
A lot of NDCA and independent events have both pro-am and amateur couples dancing together, although they are of course judged separately. My DW and I often compete both pro-am (with our respective instructors) and as an amateur couple, in the same comp. NDCA comps also have pro events, although these are danced separately. USA Dance events are, of course, amateur only. (Although their standard for what constitutes "amateur" has some loose ends.)
One can compete in single dances (each style separately) or in the multidance events and the latter is usually the 'real' competition because there are so many catagories for the former - divided by many age groups and skill levels.
In the multidances you are judged as a couple and at the highest levels its sometimes hard to tell a pro/am couple from a top am or pro one...
As for compensating the pro: It seems to vary by which part of the country it is. In the Southeast, by convention there's two parts to it: (1) You enter events through the studio, which takes a cut of the entry fees. The pro gets a cut of this as his/her compensation for the comp. (2) The am is expected to cover the pro's expenses. If two or more ams share a pro, they split the expenses. This is a good way for syllabus-level dancers to reduce costs for a comp; dancers at different levels can share a pro, and they won't have heat conflicts (assuming the comp organizer is reasonably accommodating of pros with multiple partners).
The pro's cut of the entry fee typically doesn't amount to much. However, since comps are generally over the weekend, and most pros in this area don't teach much on the weekends, going to the comp isn't really depriving them of income.