Are aestheticians - medical or otherwise qualified to do sclerotherapy, chemical peels, CoolSculpting, and microneedling?

Most states will license medical aestheticians, and the abilities and scope of practice will differ from one state to another.  

You've asked a great question, and issues in "scope of practice" are frequently discussed in the healthcare profession.  Rules and regulations vary by location.  It would be wise for you to search for an experienced Dermatologist or Plastic surgeon to perform many of these procedures such as sclerotherapy or medium/deep chemical peels.  On the other hand, I don't know any physicians performing laser hair removal themselves, as this is a procedure that typically can be done safely and effectively by a non-physician provider.

While it is legal to have these services performed by an aesthetician, it is important to consult with a board certified plastic surgeon or dermatologists prior to treatment to insure that you do not have any underlying medical conditions that could interfere with your results.  In the case of CoolSculpting,  results can be permanent.  Having a physician who is trained in all areas of body contouring, is key to determine if CoolSculpting is the appropriate treatment for you.
Edward I. Lee, MD