Was the girl's action, in refusing to be alone with the young man, appropriate, and will she be held accountable for rejecting marriage proposals due to psychological reasons?

It is permissible for a woman to offer herself in marriage to a man she deems righteous. If a suitor comes to a woman whose religiosity and character she is pleased with, it is recommended to accept him, for the Prophet, peace and blessings be upon him, said: "If someone whose character and religion you are pleased with comes to you [seeking marriage], then marry him. If you do not do so, there will be tribulation on earth and widespread corruption." This command to accept is not an obligation but a strong recommendation, so there is no sin in not accepting a suitor due to psychological reasons or others.