How can one supplicate to God and invoke Him by one's state, and does this include informing God Almighty of one's weakness and what is in one's heart, like an outpouring? Is it permissible to do so during prayer?

Seeking intercession with Allah is through His Names and Attributes, through righteous deeds, and by the servant's demonstration of his poverty, need, and humility before Allah Almighty, such as the supplications of Job and Jonah, peace be upon them. Therefore, mentioning one's condition, weakness, and complaining to Allah Almighty does not contradict patience; rather, it is a praiseworthy display of humility and neediness. It is considered a legitimate form of intercession, whether inside or outside of prayer.