Plumbing – Water Hammer from Upstairs Toilet

This normally happens near quick-acting valves in your plumbing system, like those used in a clothes washing machine. Those valves are opened by a solenoid and get slammed shut by water pressure, and all that water coming to such an abrupt stop can rattle already-loose pipes, cause them to become loose, or in the worst case damage them over time and cause leaks. That's why water hammer arrestors are commonly installed near washing machine outlets (it may be required by code, I'm not sure). They look like this:

They work by maintaining a reservoir of air inside that vertical tube. When the column of water is stopped abruptly by a valve, the air acts as a cushion, compressing so that the water can slow down more gradually and impart less inertial force to your pipes.

These are fairly easy to install even for someone with no plumbing experience. I believe the one pictured is designed to be mounted inline with a sink or toilet connection, and they also make models with standard garden hose style threads for a washer connection. You shouldn't need to install these at every fixture; one set (hot and cold) for each bathroom/kitchen should be plenty.

Since your problem seems to occur on (relatively) slower-acting valves that shouldn't be generating an unacceptable amount of water hammer, you may also just have a section of pipe that's not mounted properly. If you're only noticing the banging sound in one area, it may be possible to open up the wall there and install some pipe clamps to keep things from moving around and making noise. This would be a more difficult job than installing arrestors (but potentially cheaper if you do it yourself).

Assuming that the water does not continue to drain after it reaches the half-inch drop, I believe that what you're seeing is by design (intentional or otherwise). When the tank on the toilet refills, a small portion of that water goes to the toilet bowl to refill it. The bowl is typically overfilled to ensure the water level fills up to the edge of the siphon (I'm going to refer to it as such, even though this is not the name on many newer toilets) to prevent sewer gas leakage, and the excess drains over the edge. I suspect that your toilet is of such a design that the water level inside the siphon equalizes slower than one would expect.

There are a number of reasons that the water level could equalize more slowly; some models create a back-pressure inside the siphon, some create a positive air pocket for additional suction during the flush, or it could just be the intentional design of the siphon.

I doubt it is something to worry about.