Admittedly, I'm new to MIDI, or rather, returning to it from a long hiatus out of frustration with understanding MIDI.
 
When I'm exporting a mix with MIDI tracks, is it a requirement that all MIDI tracks be bounced or recorded as audio clips beforehand, or does Sonar just play the MIDI track through in the background (like "Processing Audio"). For example, if I create a MIDI track for an instrument, program it through the PRV, then save the file, if I don't do anything more than that, would an Export => Entire Mix play the synth track into the mixdown? If so, Sonar freezes on me, never completing the export.

   The first thing to do would be 'bounce to track' the entire project, then you would end up with a stereo (or mono) audio track of the project. Then you can export that track only (solo the mixdown, or mute all the other tracks).
   Another option would be to 'freeze' or 'bounce to track' each synth or instrument track separately. This way you can export each track individually.
   If you choose the latter, 'select' both the MIDI & synth track, then bounce. You will end up with a new audio track of that synth.
   Hope this helps!

If you are using soft synths no bouncing to track or freezing is needed. If you want to export a single MIDI track you select both the MIDI track and its audio output track for export, as mentioned above.
 
It is recommended that all your tracks are routed to master bus. When you export, you just pick Master as the export source and mute the tracks you don't want to export. Selecting nothing equals to selecting all.
 
If you're using hardware synths, I think it's best to bounce them to audio tracks but I'm not sure as I don't use them.