What is recommended for black and gray water? Especially when parked for a month or two? Any particular additives people like?

You should never open the drain valves to you have a good bit of water in the tanks. Our black tank is 57 gals so we dump dish water in it all the time to add more water. Gray tank is 110 gals and if we stay couple day or up to four days (shower, dish washing, and running the washing machine) we dump then. If overnight only we dump the gray water to drop off the weight. We use Thetford for the tanks ( no formaldehyde type) and buy this at Wal-Mart only. Never open the drain valves as soon as you park. If so the tank is now dry, stuff will turn hard in your tank, gas from sewer drain will come up into the tanks and out the roof vents. Walk around the park and you can tell the ones with open valves. Next people complaint this park had sewer gas odors, yes it did. Hope this helps.

My black tank gives me a warning when it's getting full. For the lack of a better word, it kind of burps when flushing. I always try to dump a near full black tank. The gray, I judge by time and people. Most of the time it's twice to every black tank drain. I always dump the gray tank after the Black. It help clean the lines.
After dumping, I put 4 gal. of water and exodurm or endodurm. Something like that. It's available at Walmart also and is supposed to break down the solids. Formaldehyde free as well.

I guess I do not understand the question. When parked for a month you dump the tanks when they are full. Many who park longer term will leave the grey open until a day or so before black will be dumped and then close. After dumping black, grey is run through the hose to help flush it. We do not use deodorant chemicals, opting instead to use lots of flush water and Geo Method which basically uses laundry detergent and Calgon softener.

If, instead, you are asking about dumping if parked for a month with not enough use to fill the tanks then you could add water to the black to fill it and then dump - best not to dump unless black is at least 2/3 full. When we are on the trip to our winter home tanks are dumped and cleaned the night before arrival and then used on the final day to our winter home where the motorhome is parked. There may be some day trips and weekend trips, and the tanks will get used occasionally when we are working on the unit or cleaning it. However, for the four or five months it sits we do nothing to the grey or black tanks unless we use enough to fill. Typically about the second day of our spring/summer travels is first tanks will be dumped after winter parking.

I don't mean any disrespect to the experts, but having RV'd for two decades in several types of rigs, I'd suggest this is try and see what works best issue. Sewer holding tanks, associated plumbing, and dumping techniques would not be so varied if one shoe fit all.

One thing is for sure. You had best go to Wal-Mart and buy yourself a plumber's plunger as a spare "tool."