I have a two part question regarding the osa referral process: do primary care physicians refer most or all of their patients to a specific sleep lab?

That's how we refer. As with most referral processes, doctors and their staff typically get comfortable with a small handful of specialists that they refer to most often and use them just about all the time. It's the same with testing facilities.
Yes. Primary care dr.'s don't have their own sleep labs, so if a patient has sleep apnea, or moderate symptoms of another sleep disorder, the doctor can refer the patient to a sleep medicine doctor (who has a sleep lab). Specialists are chosen for their medical expertise, good customer service, and good dr.-to-dr. Communications. However, an hmo patient will only have coverage at specific sleep labs.
PSG for OSA. PSG FOR OSA most doctors may have a preference for who they believe is the best sleep lab. But often times the choice is limited by an insurance plan. So it is a case by case basis.
Yes. Sleep studies can be done at home or at a lab. It depends on insurance coverage and convenience.