I truly believe that if a person is mentally ill and completes suicide (I don't say "commits" because I don't believe in this case that suicide should be considered a crime) that God will understand and forgive them. However, I know of people who have killed themselves in an effort to get even with someone or make someone feel bad, and I do believe that this is an unforgivable sin, because they never had the chance to ask God's forgiveness (asking ahead of time doesn't count). I hope this helps. Religion can be so confusing because of so many different beliefs and translations of what people think the Bible means.
Taking your own life is a sin and I believe that these people face punishment even in death. I think that hell exists and such people would probably go there because they broke one of the Ten Commandments.