Hey, TitanicWreck.
I wouldn't recommend fasting.
First, one of the challenges when dieting is to try to keep your metabolism up--it tends to slow down in response to consuming less calories. Makes perfectly good evolutionary sense, but not so useful in a contemporary environment when instead of being scarce, food is not only plentiful, it's calorie-dense. The best ways to keep the metabolism going are by only cutting calories a bit below what you need--that is, not having the drastic cut in calories you would get from fasting--and by exercising. (I'll come back to your comment about not being able to exercise in a second.)
Second, when we let ourselves get too hungry, our body tells us "I need food now!" So, fasting every other day would leave you hungry, and tend to trigger cravings. For myself, willpower only goes so far. If I'm hungry and getting cravings, I can only resist for so many days before I give in and binge.
Third, in addition to calories, you want to meet your nutritional needs. I think it would be very, very hard to do that if you are fasting, say, 3 days out of the week.
It's boring advice, we've all heard it, but still the best advice is eating a healthy diet with less calories than you would need to retain your weight.
In terms of exercising at your weight, the real measure is what your body does to cope with the exercise, not what it looks like externally. For an athlete, even a jog might barely get their heart rate up. However, for someone who hasn't exercised recently, going for a stroll at the mall might increase heart rate, and therefore have cardio benefits. The main goals for a starting exercise plan should be, I would think--low impact (you don't want to do anything that would cause injury, and thereby cause you to stop exercising); and doing just enough to get your heart rate up a bit, whatever that activity is at your current fitness level. Obviously, checking with a doctor first is always recommended. And there are people on this board with a lot more knowledge of exercise than I have--so you'll probably get more specific advice. But I do know the goal is not to do something that looks like exercise, but to do something that makes your body respond like an exercising body. If that's a stroll, walking in a pool, whatever, that's a great place to start.
Best luck with this.