Is it possible that if a person were to commit suicide due to having a psychotic state of mind, uncontrollable actions, and extreme emotional unrest or distress, that God's grace could save them and they would go to spend eternity with Jesus?

If we're talking about a Christian, it may be possible. Christians can become unstable mentally (like anyone else) and take their lives; I would be surprised if the Lord did not receive these poor, confused souls with mercy. Eternity with God is the reward for those who are in Christ.

If we’re talking about a non-Christian, it does not seem likely. The Lord takes all things into account, however, and punishment varies depending on knowledge, access, etc — all the 15 or so factors covered in my book, What's The Truth About Heaven & Hell? Of course there is another class of person: the one who is mentally or emotionally unable to understand the gospel (traumatic head injury?). We leave such persons in the hands of God. We know that he will be fair.

Sin is the problem, forgiveness is the solution, and this is found in Christ — in trusting him. Not in trusting ourselves.

Lastly, either way, any idea that anyone who commits suicide would be rewarded for taking his or her life must be rejected.