Just came home from playoing first time, so i hopy my question is not too dumb.

We weren'T sure if a Ship can be mustered in every area with a stronghold/castle, or only in those areas where there's also a port (yes, we knew it can be placed placed in the port connected to the mustering area or in an adjacent sea area, but is the port necessary for mustering the ships altogether)

We compromised that a ship may only be built in a port, so for example the Eyrie couldnt muster ships although its on a coast aream, but I'm not quite sure if that's correct.
On a second Note. Does a port count for the complete area (this actually is only important for winterfell) or just the coast where it's positioned. We compromised, so that Winterfell could muster into the Bay of Ice but not into the Shivering Sea, because the Port is drawn on the side of the Shivering Sea)

Any area adjacent to the sea can muster ships into that sea area (provided it does not contain enemy ships of course). This is a common misunderstanding due to some unfortunate ambiguous wording the rules. They mention both a mustering area and a port, then use the phrase adjacent sea area without specifying what it needs to be adjacent to. However if you look in the mustering example in the rules, it shows an area with no port mustering ships into the adjacent sea area.

For your second question, each port is only adjacent to one sea area. So Winterfell can muster ships into the port or either sea area, but ships in the port can only march, raid, support, and be raided by the Bay of Ice.