First make sure that there are no water/moisture problems, you may have to install a sump pump, or a de-humidifier to get rid of unwanted moisture. Per code the ceiling hgt must be at least 7 ft, All rooms (except bathrooms and laundry rooms) must have at least one window; Bedrooms must have an egress window (a window large enough for occupants to escape in case of fire, if the outside adjacent grade level is too high, an exterior window well with an escape ladder is needed). Bathrooms need an exhaust fan if no window is provided. The ceiling at the perimeter walls must have fire stopping.
The new stud/sheetrock walls at the existing foundation walls must be insulated, and you should leave an inch air space between the foundation wall and new wall. It is more practical and less expensive to install tiles instead of sheet rock on the ceiling, sheet rock looks better, but acoustical tiles allow easy access to piping, wiring, and duct-work.
The new Bathrooms waste piping may require an uplift pump if the existing house waste line is above the level of the bathroom floor. Smoke and carbon monoxide detectors must be installed per code.