You likely have PVC plastic waste pipes that are behaving correctly, and noisily.
They are tightly secured to the wall framing. When they expand from hot water (get longer) or contract and cool off (get shorter) they slide along the wood framing they are secured to. The temperature change from hot water draining through them causes a rapid expansion of the plastic pipe, and a plastic to wood framing “earthquake”. This earthquake is a “bump” noise or ticking sound as the pipe gets longer with the warmer water flowing through it. When the hot water stops draining through the pipe, then the pipe gets shorter again as it returns to a neutral temperature and size.
When the house was built the plumber tightly secured these waste pipes, and they jump or rapidly slide against the wood framing … which makes the sound. I call it an “earthquake” because it happens in an instant and not gradually. This instant move causes the bumping sounds which happen both when the warmer water begins to drain and again as the pipes cool off.
The solution is to cut open your drywall and loosen all the clamps inside the wall so the pipe slides smoothly along the wood framing, then close up the drywall, finish the drywall and paint. This is not usually not worth the effort because the pipes are not causing any damage, only sounds. Consider the wall noise as the personality of the house and live with it, or do open wall surgery to stop the noise. It is highly unlikely that damage is part of this occurrence.
The changing water temperature is related to an absence of pressure balancing shower valves which regulates pressure to adjust water flow to the shower when other cold water uses take away the flow from other fixtures.
This shower pressure balanced valve cuts the hot water flow down when the cold water pressure drops, usually from flushing the adjacent toilet in the same bathroom or in your case in an adjacent bath.
Think this through with me for a moment. Hot and cold water supply pressure are equal when no fixtures are turned on. This is because all water pressure comes from the cold water supply from the water company line in the street. When hot water is turned on and flow begins the water pressure drops on this hot side….it’s like having a hole in the hot water pipe. This is not usually noticeable unless someone is in the shower where 5 degrees of temperature change is really noticeable. This flow/pressure drop often happens to the cold water pressure when the toilet is flushed…a shower user will be scalded because the cold water is reduced from the flow to the shower.
I believe your choice is either to change the shower mixing valves to the newer pressure balanced type for more even temperature showers or stop using other fixtures at the same time.