You won't get cavitation in a domestic heating system, especially with the pump on setting 2.
You shouldn't get air trapped either. There may be a partial blockage. Try a magnet against the pipes at the top right of
picture 1,
where the feed pipe joins, especially.
For your shower, make sure its hot supply gate valve is full open (less half a turn!), and try progressively closing the cold supply valve. It won't hurt the pump to run with a dead end for a quick test.
You should find you can take the shower valve apart from the front. Bits of dirt can easily stick in there, or the catridge may need changing.
SUpplying the hw side of the pump from somewhere on the pipes is ok IF the supply to the hw cylinder is low resistance. It often turns out that 22mm is too small, so it's easier for the pump to suck air down the vent pipe.