As others have pointed out, those are roller brakes, not discs. It's a good idea to make sure they were greased from new. I sold a couple of bike models with roller brakes that were dry from new. (Shimano Roller brake grease only!)
The play you are experiencing in the front when you apply the brake and rock the bike is probably the slack where the brake reaction arm fits in the slot on the fork. Not unusual with these brakes and nothing to worry about. It does make detecting headset play a bit difficult though.