1. Yes, assuming that the sea zones the transport loads in and has to pass through on its way to offload are friendly and the sea zone in which it offloads is either friendly or is made friendly through sea combat.
2. Yes. You may fight as many battles as you wish on your turn. However, all combat moves must be completed before any combat begins, and each unit may fight in only one battle (although air units may be fired upon by multiple AA guns along their route, and units on transports may be indirectly involved in a sea battle before offloading for an amphibious assault).