Ammonia should be 0 but apart from that it seems ok dont worry about the no3 no matter waht people tell you. You are always going to get Nitrate if it goes anything above 20 then you start to worry only a little though.
Removing ammonia will inhibit the bacteria that get rid of the ammonia from growing, so cycling will take forever and adding a fish will result in an ammonia spike because you never allowed that special bacteria to fully establish. Don't use chemicals unless you need to treat for a disease.