Is someone who committed a sin while mentally ill punished, and will God forgive him after repentance and remorse for changing his disposition, especially with the illness persisting despite supplication and prayer?

Sincere repentance is accessible to every servant by seeking refuge in Allah Almighty, confessing one's sins, feeling remorse, seeking forgiveness, and humbling oneself before Him. You hastened in changing your gender, when you should have been deliberate. Allah Almighty has promised His servants that He will answer their supplications if they supplicate to Him with sincerity and humility. He praised Himself as one who answers the distressed. The immediate absence of the effect of a supplication does not mean it has not been accepted; it may be stored for a greater good or to avert harm, as in the Hadith: "There is no Muslim who supplicates with a supplication in which there is no sin or severing of family ties, but Allah gives him one of three things: either his supplication is answered immediately, or it is stored for him in the Hereafter, or evil similar to it is averted from him."

Worldly success is not a sign of Allah's pleasure, nor is tribulation a sign of His displeasure. Allah tests His servants to see who is grateful and who is patient. Turn to your Lord, seek His help in your hardships, and have a good opinion of Him, for "with hardship comes ease."