So much depends on local custom and environment! On boats, as Art2K said, and in many RVs, there is a covered receptacle (ours is a coffee can, covered with adhesive backed paper, and replaced fairly often) for paper. It is lined with a plastic bag. It is changed when necessary, but ours has never smelled before getting full enough to change. Generally, when it's full, the bag is replaced, the full one goes in the trash, and the trash goes to trash-land. On boats at sea, there is generally an isolated area where trash things that cannot legally and safely be jettisoned (non-organics, mostly, and particularly plastics) are stowed in double bags until there is a proper place for disposal. The use of water for cleansing (when possible) and minimal amounts of paper, or special toilet wipes, is also encouraged as providing less waste for the can. In desert areas, cabins, summers, droughts, wells and so on, the "let it mellow" rule often applies -- usually accompanied by "nothing in the head you haven't eaten first" so no paper.
In some countries, the plumbing is absolutely not designed to take paper or anything other than human waste, and if there is no paper receptacle, it can accumulate in a corner of the room, which is what people do with it (I find this icky, but the bathrooms are cleaned often, and it's the local custom, so I cope.)
Place a clean brick in the tank of a regular toilet, according to our water department, and turn your regular toilet into a lowered-flow one.
I suggest the "flush or not" rule generally is a "local knowledge" thing.
At night? In a house where I have not been asked not to flush? I flush. At home, I don't like being awakened by flushes during the night, and if the seat lid is down (and I always keep them down) when I enter a bathroom in the morning and especially if we have guests, I generally flush before peeking if I am unsure. Our house is old and the bathrooms don't have fans. If you might leave odors behind, not only would I appreciate it if you flushed, no matter the hour, it would be nice if you opened the window (we have those) and looked around for the air freshener. I bet there is some close at hand. There is in our house.