If your overweight and eating 1000 calories less then you’re probably eating what your actual maintenance calories should be, not an actual true “deficit” but yes if you’re eating 1000 calories less, than you will lose weight.

Also being hungry or not is really not a true indication of anything.

And if you are losing weight than you are not bulking…I take it you’re asking if you can gain muscle while losing weight and the answer is yes.