Major loss of appitite, losing weight too fast

YES this is pretty bad you need to be eating at least 1200 calories, 600 calories a day plus exercise is very unsafe. You aren't fueling your body enough! You might have to force yourself to eat.
Ensure shakes are very good for this, its like a meal in a shake so you can drink your meal instead of forcing food down your throat.

Yes that is not enough food. Are you sick at all? You body has a certain number of calories that it must have each day to just do the things that keep you alive. For example, hormones, enzymes etc. This number is your Resting Metabolic Rate. This number is usually around 1600 calories (that is only a guess every person is different) . If you consistantly take in too little calories your body will view that as a threat and will try to store anything that you take in because it thinks you are starving. The weight loss you are seeing is not sustainable and is most likely attributed to water loss andyour body breaking itself down to maintain your body systems. Try eating less amounts much more often through out the day. That may help, also try and take in at least half of your body weight in fluid ounces of water each day!
Good Luck!

The great thing about MFP is that you can trust the process. Whether your tendency is to overeat or undereat, if you make a commitment to stick to what MFP tells you to do and be consistent with it, things will begin to fall into place. Please, for the sake of your health, trust MFP and not your appetite to tell you how much you need to eat. Good luck!

I know when I get really stressed my appetite goes down dramatically. Just try to remember to eat even if your not starving. I find small snacks help a lot.