I occasionally add ice if I feel that my sensors are gunked up. Not sure if it actually does anything, but it doesn't cost me anything (use ice from home) and makes me feel better.
OP, I usually stand on the flush pedal for about 10-15 seconds before we use the toilet at a campground. The biggest issue is to use sufficient water when you flush and sufficient water when you drain your black tank. If you are at sewer sites, use plenty of water. If you are without sewer, use plenty of water to start, and you can be more sparing once the tank has a decent amount of water.
I don't really use chemicals. My wife likes them, so I either drop a baggie down or else I tell her that I did. Not sure either one of us has noticed a difference if drop a baggie or not... :)
Congrats on the trailer and hope you have a LOT of fun. I miss the days of a simple camper. We've got 2 kids and 3 dogs now... 31 foot camper with a big slide, etc. I miss a small simple trailer and the simplicity therein!!!