I think you have two distinct problems here. I agree with the good MBDOC that you have a mono-valve problem. The mono-valve controls the admission of hot water into the heater. They're known to fail, in which case you get heat all the time, whether you want it or not. The good news is a repair kit is ~$25 bucks and installation is about as easy as it gets. BTW, only the outside vents are heated - it's not possible to get warmed air out of the center vents.
However, your a/c also sounds as if it is weak - probably very low on freon. The a/c system of a car can remove heat from the air at a certain, relatively fixed, rate. If you pass a little air through the system, that air is cooled down quite a bit. Pass a large volume of air through the system - by running the fan on high - and the air is cooled only a few degrees. In either case the same number of BTUs are removed. Anyways, you should have the a/c system diagnosed by a good shop. Have them check for leaks and top up the system.