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.
How long will my stitches (sutures) take to dissolve? The time it takes for dissolvable or absorbable stitches to disappear can vary. Most types should start to dissolve or fall out within a week or two, although it may be a few weeks before they disappear completely. Some may last for several months.