بسم الله الرحمن الرحيم
(1) There is no need to give three talaqs; it is a sin to give three talaqs together. Hence just giving one talaq bayin is enough as it shall terminate relation of nikah completely.
(2) If your friend did intercourse with his wife or met her in privacy after nikah then it is necessary to pay full mahr. You may adopt any method to pay the mahr amount. Yes, if the girl remits some part of mahr or full mahr then it shall be remitted.
(3) Your friend had not given talaq to the girl then her nikah with the other person was not valid. First your friend should give her talaq and separate her from his nikah as well as he should inform her. He should also inform the girl that her nikah with the other person was not valid. Now she should complete her iddah after he has given her talaq and then do nikah again. Or she should ask any alim about her case and act accordingly. However, you should give her talaq and make her free so that you could not have share in sin.
Allah knows Best!
Darul Uloom Deoband