Big Mumma, now that you're in your third week you are in a good position to start exercising (as Clairejen says, you mustn't start anything new in the first two weeks) but make sure you start slow and keep the intensity low while you are on a VLCD. Resistance exercise is excellent, as is any kind of low intensity cardio (aerobics, swimming, walking etc.) and flexibility work (pilates, yoga etc.). A combination of all three types will give you a well-balanced regime, but the most important thing is to find something you enjoy, because if you hate it, you won't stick to it, and why put yourself through something you hate?
As for getting hungry, that's why you must make sure you don't overdo things - if you overexercise then your body will NEED more food, so you have to strike a balance. Anyone who wants to do a lot of high intensity exercise needs more in the way of calories than SS, AAM or 790 can provide - to be honest, for strenuous exercise, you should be on at least 1500 calories.
You absolutely must drink extra water before, during and after a workout - take a drink at least once every 15-20 minutes during exercise and make sure you drink about one and a half times what you have lost e.g. if you lose one kilo during exercise, drink a litre and a half of water to rehydrate.
Just a couple of things I need to point out, too:
Sweating is your body's way of cooling you down. Some people sweat loads, some hardly at all. Quite often, the harder you are working, the warmer you are and the more you are moving, the less you seem to be sweating because it's evaporating almost immediately. On the other hand, while doing something like yoga you may sweat loads because you're staying in one place and the air isn't moving around you. Please don't use sweat as an indicator of when to stop, because it's no indication of how hard you are working. Being able to comfortably hold a conversation during a workout is probably a better guideline.
"Toning" is a myth - there is really no such thing. "Toning" is just a combination of losing fat and gaining muscle. There are effectively three types of resistance training - endurance, strength and power. When people talk about "toning" they generally mean endurance training, which is the type where you use lower weights and do higher reps. If you are taking in sufficient calories and protein this will still result in building muscle (as clairejen rightly states, this isn't possible on a VLCD), but you will improve your endurance rather than your strength (ETA: actually you'll improve both but the focus is on endurance with this type of training). As women we do not produce enough testosterone to build muscle quickly anyway, so without the help of steroids or an incredibly intense training programme, we are never going to "bulk up".