Can a person who is mentally ill be forgiven for suicide?

There is no passage in the bible, saying suicide is a sin.  The early christian church said it was a sin because they wanted to deter it.

We know that God loves avery human being perfectly, and therefore equally. What loving parent would hold their child responsible for something that was beyond their control?

that's not our call ...................................

Even though taking one’s own life is a serious sin, God fully understands factors such as mental illness, extreme stress, or even genetic traits that may lead to suicidal urges. (Psalm 103:13, 14) Through the Bible, he provides comfort to those in distress. In addition, the Bible says that there will be “a resurrection of both the righteous and the unrighteous.” (Acts 24:15) This shows that there is hope of a resurrection for people who have made serious mistakes, such as having committed suicide.

NO ONE HERE OR ANY WHERE CAN JUDGE ONLY JESUS IS THE JUDGE. 

Yes,of course.
They are not in their right mind.

Well no one in their right mind would do it would they...?

This is Psychology. We talk about things that help with suicidal feelings. There's a lot of things that can help. Click on my name for advice from experts about depression.

Although I know almost nothing about you, I’m willing to bet that things aren’t as bad as you think they are. You’re looking at things through depression glasses, which make everything look worse. When you recover, things will look very different. Problems that seemed hopeless will suddenly have obvious solutions. You’ll appreciate things as you never have before.

The most important thing is knowing how to cope in a moment of crisis. It's very important to calm down. This will make you feel better and let you think clearly.

A very easy way to calm down is just to breathe slowly. A doctor recommends inhale to a count of 4, exhale to 6. You'll feel better in 5 min or less.

Also, simple distractions can be very good. This video has suggestions. It also has a very good hotline. No one will bother you if you call.

https://www.youtube.com/watch?v=1yBXl81QPyY&t=7s

I'm curious what other kind of person even does it? 

That all depends on the forgiver. Some will forgive it. Others won't. My uncle killed himself in 2006, a couple of years after a bicycle accident resulted in a head injury that made him schizophrenic. I loved him more than anyone else in the whole world. His suicide devastated me, tore a giant whole right out of my life. I know he was mentally ill, but knowing that doesn't keep me from still welling up with anger at him, anger for refusing treatment because he would not be helped, anger for not wearing a helmet that day when he always insisted everyone wear a helmet, anger just at him not being there and abandoning me, anger so immense that I can't even always point a finger at it and it's just generalized anger, so I struggle to forgive him. Some days, I do forgive him, have forgiven him. Other days, no, I'm too angry. It's a process.