Is there plastic surgery for free?

Yes. Plastic surgery may be performed by plastic surgeons on a pro bono basis for patients in need. There are a number of foundations and charities which help facilitate this for victims of domestic violence, veterans who sustained injuries in combat, or children with congenital birth defects. Discounted aesthetic plastic surgery is available through some teaching institutions.
No. Plastic surgery is a broad discipline which includes reconstructive surgery, which in almost all cases is covered by insurance, and cosmetic surgery, which is usually associated with out-of-pocket fees and expenses. There are surgeons who donate their time and services to provide surgery for people who cannot afford it and who have no medical insurance.
Case by case basis. Cosmetic surgery typically has a cost associated with it. Reconstructive surgeries may be done on a pro bono basis. Regardless, please choose a board certified plastic surgeon who does at least 100 of those surgeries every year.
Yes . Plastic surgery may be provided for free on a compassionate need basis but usually when the need is reconstructive and not typically for cosmetic reasons. Plastic surgeons often volunteer their services to communities for such purposes as gang tattoo removal, cleft lip repair, domestic abuse victims, breast cancer reconstruction, the shriner's hospitals, etc.
Face to face . There are several organizations that provide plastic surgery pro bono, including face to face, which provides for victims of domestic violence and abuse.
Try residents clinic. In addition to charities, foundations, pro bono work you can try some academic teaching hospitals where you can have clinics run by plastic surgery residents for free or a very reduced price.
Yes. If plastic surgery is reconstructive then the insurance may cover it, of course you must have insurance which is not free.
Free. Cosmetic plastic surgery is a fee for service practice. Reconstructive plastic surgery is often covered by your insurance carrier. There are some teaching institutions that offer discounted treatments and surgery so the residents can gain experience.
In certain circumsta. The previous answer givers a good overview of what is available but there is no consistent source. Most plastic surgeons receive messages or letters from patients hoping to be able to have surgery such as a tummy tuck or breast surgery because the patient can't afford it. This doesn't fall into the same category as the domestic abuse, etc. Category and rarely is performed i would imagine.
Sometimes. Plastic surgery includes reconstructive, microsurgery, burn surgery, hand surgery, cosmetic surgery, etc. With elective cosmetic surgery the patient pays out of pocket. Reconstructive surgery may be paid out of pocket, by some insurances, or charitable groups. It all depends on the situation. Teaching hospitals may do work at a lower cost. A board certified plastic surgeon may be able to help.
Not generally. Elective plastic surgery is never free. For deformities and injuries surgery is not infrequently done free through an ER on call surgeon, or through various charitable organizations. One of these not active in the US is Depilex Smile Again, providing free burn treatment in the Middle East. You might check with a social worker or a health department.