Old Ways Are Best!
3. Can you build a ship if there is no built port tile in the connecting cities? The rule that states you need to have at least a rail connection into the city would seem to allow this.
A Ship cannot be built unless a constructed port (anyone's) is in place that is connected to the ship space. If you are using a "Location" card then that is the only prerequisite.
If you are using an "Industry" card then the port in question must be yours or, if it is not, then you must be connected by rail to the port city. That, I believe, is what is behind your second sentence.