1. No - as a fact, there is no such thing as "心理醫生".
And they are not doctors as well (as they are known as psychologists).
2. Yes.
3. Totally different. You don't have to have a mental problem to talk to a psychologist (for example, some people talk to psychologists for marriage/relationship issues).
Psychiatrist is the medical doctor who treat mental illnesses.
4. It depends.
5. You will have to find it yourself (as there are not very popular in Hong Kong).