Yogurt is a mixed protein/carb, which means that there is a block of protein and a block of carb per 1/2 cup serving.
Mozzarella cheese does not contain a lot of carb, so it really only counts towards the protein block (and the fat block, if you want to take it that far).
Cottage cheese is counted the same as other cheese, basically just as a protein block. However, there is a bit of a difference in that it does contain a bit more carb than other cheese, so if you eat 3 blocks of it, you may actually have enough carb to be counted as a block. I usually take this into consideration when I use larger amounts of it. But, it depends on your level of carb-sensitivity. Most people will probably not be affected by the additional carb, and do not worry about it.
Remember, the Zone is just that... a zone (not an exact point). Think of a parking zone. There are boundaries, but as long as you park within the lines, you are in the zone.
As for me, I think that the most satisfying protein out of the ones that you mentioned in your post is the cottage cheese. But, that is just me.