Will the deceased be held accountable if things they used to do that were forbidden or wrong are mentioned? And in the life of the Barzakh, is there accountability, or merely the questioning by the two angels? And how do supplications benefit the deceased before the reckoning?

Your mention to the psychiatrist of the prohibitions committed by the deceased will not increase his accountability or punishment, for Allah Almighty says: "And every soul earns not [consequences] except upon itself, and no bearer of burdens will bear the burden of another." You may mention this to the doctor if you need it to seek treatment for a psychological illness. However, if there is no need, it is not permissible, due to the Prophet's (peace be upon him) saying: "Do not curse the dead, for they have gone on to what they have sent forth." The life of the barzakh involves questioning, which results in either bliss or torment. The grave is either a garden from the gardens of Paradise or a pit from the pits of Hell. Supplication for the deceased benefits them by elevating their status and increasing their bliss, or by lifting their torment.