As I understand metabolic adaptation it means that if you eat below a certain amount (I'm not sure there is any one magic number) that your metabolism slows and so you lose less weight than you would have lost had your metabolism not slowed. It doesn't mean, however, that you don't lose any weight at all. If you eat fewer calories than your slowed metabolism burns then you will still lose. You might be losing more slowly though.
The bigger concern with only eating 700 or 800 calories is that it is hard to get nutrition when you eat that way. On the menu you gave I'm not sure you area really getting all the vitamins and minerals that should be eaten for good health.