Sounds like you have a leak, probably from the flapper valve into the tank. To confirm this, put some food coloring in the bowl. Let it sit overnight, and I'd bet that the bowl is clear by morning. The only way that happens is if it gets flushed out. Replace the flapper valve and it should fix it. Also, check the seat where the valve sits, make sure it doesn't have anything on it - it should be smooth without any pits or debris. If it is, they make replacement seats you can put in. Did you have to move around the chain that pulls up the flapper valve? It needs a little slack, it may have been kinked and is holding the flapper up a little (it doesn't take much). Give it a little more slack, or unkink it. Last, make sure that the fill is to the design height.
The banging of the pipe when it shuts off is because this kind of valve shuts off quickly. Typically much quicker than the old style ones. Water wants to keep moving, and when you shut the valve off quick, anywhere the pipe may not be anchored properly, it will jump. It may be hitting a wall, or against a loose bracket. They make water hammer arrestors that act like shock absorbers to cushion that water column. They work well on washing machine supplies and things like that as well.