When I first bought my MH the salesman sold me some chemicals. I faithfully used them for a while and then realized that maybe I was just wasting my $$$. I Stopped using the chemicals, and haven't used them since.
After dumping I add 2-3 gallons of water to the tank. I don't add extra water to the tank after using. I did install a Tornado tank rinser several years ago and use it every few weeks, don't know if it helps or not. I dump when it is over 2/3 full. If it is not at least 2/3 full when I want to dump, I add water. After dumping I start the procedure again. I have always used the same TP that we use in the house, nothing special.