Do you have fish in the new tank if not then the beneficial bacteria will quickly die if it does not have a sorce of foor i.e ammonia, as for where to put it not too familiar with the filter but i would imagine the large compartment. Sure someone who is more familiar with the filter can help you. Also if you have filled the new tank with tap water leave the old media out for at least 48hrs so that any chlorine and Chloramines present will not kill the bacteria. Good Luck
As previously mentioned it is to do with the hot weather i've had the same problem mine too is at 20ppm. I called the local water board North West and they said it was normal during this weather. So take previous advise and condition your water before adding.
Unlikely buut you should always use a gravel cleaner and keep the substarte clean. Problems associated with a dirty 'tank floor' include bacterial infections and you are creating a breeding ground for parasites.
It depends on how long the tank has been set up, filtration type and what your water parameters are but i personally wouldnt add any more, it is much easier to manage a tank that is under stocked or correctly stocked rather than living on a knifes edge by taking a tank to its maximum fish capacity.