1. In at least some U.S. jurisdictions (and possibly all), lawyers' practices can indeed be set up as corporations; my former firm was an example. The individual lawyers in the firm are still personally liable for their own malpractice and for that of any junior attorneys and/or staff whom they supervise. The corporate form does protect them from personal liability for the office lease, etc., unless they've personally guaranteed the lease, which is not uncommon. (Don't know how it works for doctors but I assume it's similar.)

2. "C corp" is an income-tax classification; AFAIK it has nothing to do with non-tax liability.