Morning Pfc Pander.
1.You are correct. A naval battle precludes a naval bombardment.You cannot split your force and do both.
The only time he could choose to bombard, is if the naval unit was a Sub or Transport, as they do not make the SZ hostile. He then could choose to either sink the ship with all his navy(never some) or ignore it and bombard.
2. No. If the Cruiser is in SZ60, he could not reach SZ 62 to amphibiously land, as you have successfully blocked his direct path.
If he owned Shanghai, he could drop units there in Non Combat after eliminating your Cruiser in the Combat round.
I think I have understood this is not the case.
Please ask again if unclear or if your friends doubt you.
I hope you have many fun games ahead.