Are there clinical studies of cosmetic surgery available to get procedures done?

Yes. The american society of plastic surgeons asps www.Plasticsurgery.Org and the american society forvaesthetic plastic surgery asaps www.Surgery.Org, have extensive studies and statistics for these procedures.
Yes. Yes there are a variety of clinical research trials going on at any time seeking suitable candidates for study recruitment.
Yes. Many residency programs have ongoing studies. Procedure rates might be reduced, but not free.
Yes. Most high volume academic surgeons have some kind of retrospective study to evaluate different tecniques used in cosmetic surgery and ways to improve their long term result.
Yes. Occasionally studies are done which includes the delivery of care for the volunteers. Best examples deal with liposuction studies dealing with stem cells. Patients have volume of fat removed, and the fat studied in a laboratory. The patient does get either reimbursement or no cost surgery treatments.