Plans are generally not necessary to get a permit to do mechanical work on a dwelling. You will be expected to briefly describe the work proposed. For example, describe the appliance you intend to install and whether you will be installing a new vent, new ductwork, etc.
It depends on what kind of stitches the dentist used in your mouth. There are two types: stitches that resorb on their own and you don't need to do anything, and the other are stitches for which you see the dentist in about two weeks and he/she removes them. Ask your dentist which type he/she placed in your mouth.
Advances in dental care have rendered gum surgery unnecessary in most instances, when compared to 10 and 20 years ago. Non-invasive treatment (without surgery) for moderate and many forms of advanced gum disease is now the normal course of treatment, rather than the exception among dentists such as Dr. Caputo.