Questions regarding Bourne Identity [closed]

I always assumed the "doctor" to be a regular member of the fisherman crew who just happens to know something about medics too. Seen in that light, the relationship between the two had little to do with a normal doctor-patient relation wherein the doctor could order the patient to stay.

In this case, Jason was eager to find out about himself and to go to Zurich. The doctor did not "let" him go. Jason just went, as he needed no permission nor release card.

Also, the time spend aboard healed his physical condition. On mental health, the only thing the doctor could do was wait and observe. Something both of them would not have had much pleasure in, I imagine.

On your second question, assuming the fishing boat moored somewhere in the south of France or Italy, obviously Europe's Mediterranean Sea anyway (and the filming locations say it is Imperia, Liguria, Italy): according to the Schengen Agreement, traveling between its European member countries is without internal border controls. So all he needed was a plain train ticket that can be bought with cash money. In most European countries, there are identification requirements though, but normally you have to provoke them to get them to ask you for it.

Without knowledge of traveling within Europe, it sure may need a little guessing on how exactly he got what he needed. The only hint the movie tells is the doctor saying:

It's not much, but it should get you to Switzerland.

With Jason not asking how to, but instead saying just "Thank you" for the money, and the resourcefulness he later on exhibits in the movie, we might simply imagine that he just managed.