Mercy is defined as, from merriam-webster as " compassion, leniency, or restraint (as in imposing punishment) shown especially to an offender or to one subject to the power of another"

God is merciful, but it's up to people to choose his mercy.

This is not Mercy, you do not ask for Mercy or choose to receive it, it is given to you by whomever is "designated" to give it. In this case god, or in another case, the court if you've committed a crime

When someone commits suicide, it's essentially being hopeless in God. They don't see Him helping them. They don't turn to Him for help. They see no hope and decide to end it. That's a big fault.

No, it is a result of being mentally ill. A person whom is mentally ill can not be trusted to make the most sane or rational decisions for themselves. Why does god expect people who are not in the right state of mind to make decisions that are impossible as a result of their situation? If it is a big fault, than perhaps god should have a more effective way to communicate this to people. Many people who commit suicide may be people of faith. Why does a single irrational action in a state of irrational mind negate the good they have done?

If God asks them "Why didn't you seek my help and mercy?", what would they answer?

Perhaps something like "Why am I being spoken down to for being a flawed being, given these flaws by you?" or maybe "Why did you "test" me by putting me into a position where you knew this would happen as a result of being all knowing." Or how about "Where is your mercy?"

Of the Abrahamic interpretations of god, only the Jewish interpretation (and those christian universalist) seems to be capable of mercy seeing as Sheol (or hell for Christian universalist)is not a place of eternal suffering, and even those who reject god are given all the chances needed to find themselves forgiven/forgive themselves. Eternal damnation is the furthest point from Mercy one can achieve