Is a wife forbidden to her husband who committed sodomy while married, then repented? And what should he do to get rid of suicidal thoughts caused by his guilt?

Sodomy is one of the gravest sins and indecencies. Allah accepts sincere repentance from it, for sincere repentance erases sins and replaces bad deeds with good ones. The conditions for accepted repentance are to abandon the sin, regret it, and resolve never to return to it, while seeking Allah's help and relying on Him, remembering the Hereafter, avoiding the company of the heedless, and striving to associate with the righteous.

As for your intention to kill yourself by suicide, it is forbidden by Islamic law. The implementation of punishments is the responsibility of the Imam, not the individual, and one must conceal oneself when falling into indecencies. What your friend said, that the wife of a married sodomite becomes forbidden to him, is incorrect.

You must strive against your desires, distance yourself from bad environments, draw closer to Allah, and beware of despairing of Allah's mercy, for despair is a characteristic of the misguided and the disbelievers.