All transactions are permanently stored in the blockchain.
A blockchain explorer in blockchain.info
Everyone can see the transaction of every public address
Ok interesting point and perhaps the word
public.
So what you are saying is if I put a public address in search I can see every transaction including the addresses the bitcoin went to, correct.
Secondly you say public, when opening the wallet at blockchain and address(es) a box popped up and asked if I wanted it to be
public. I did not check that box off, was that a good idea, is this the public you speak of.