What is the ruling on intimately supplicating to Allah and complaining to Him during prostration by saying: "O Allah, I am poor, so enrich me; O Lord, I complain to You about such and such; O Lord, my condition is such, and I desire such and such"? And does that invalidate the prayer?

It is permissible to supplicate to Allah, engage in intimate communion with Him, and complain to Him while prostrating, for the needs of this world and the Hereafter, as long as it does not reach the point of transgression in supplication. This does not affect the validity of the prayer.