Is a relationship with a girl, going out with her, and talking to her, forbidden?

As long as you have not entered into a marriage contract with this girl, she is a stranger to you (non-mahram), and it is forbidden to mix with her or to be alone with her (khalwa). Similarly, speaking with her over the phone is forbidden if it incites lustful desires. You must immediately sever this relationship and propose to the girl through her family. Marriage is the solution to what you have called a "non-forbidden relationship," when in fact, it is forbidden by Islamic law.