We also use Dawn, both at home and in the TT....also agree that if it's good for the baby ducks, it's good for Rocky. TP?....we just use the cheapie, single ply and have never had problems. The water/dissolve test is a good one and you'll know quickly if your product is ok.
From time to time, I will use the treatment for the grey tank. Can't recall the exact name, but it's available at Walmart as well as the big camping supply places...sort of a lemony fragrance and supposed to be good for the seals. My main use is if we have anything seafood, I don't worry about getting the fishy smell. It's not a pricey item and I just feel better using it from time to time...also if the weather is terribly hot, minimizes the odor chances.
Re treatment for the black tank, we have used Odorlos for several years and very pleased with it. Sometimes a bit of a challenge to find it....CW carried it, then they didn't, then they did, hope they still do. The Geo Method, which many use, is easy and inexpensive. We likely will give it a try next spring.
Only 2 trips left this season and then the pink stuff....darn! Weather permitting. Had to cancel for this past weekend due to heavy rains, etc and just hoping for the next 2 weekends to work out. Normally we winterize just before Thanksgiving, allowing us another weekend or two, but we're so far behind on everything house-related that we just have to get ourselves in gear around here. "Merry Maid" and "The Yard Man" seem to have forgotten us, so.....
Enjoy your first outing with the new TT. Remember to take a paper and pencil to jot down everything you realize you need or don't. Happy Camping!