Is the prayer of a servant who commits major sins and asks God for that which would help him repent (such as marriage) rejected because he is disobedient? And is one of the conditions for the acceptance of prayer piety and closeness to God?

Obeying Allah and responding to Him are among the reasons for the acceptance of supplication, while abandoning His obedience is among the reasons for its rejection. However, this does not mean that a disobedient person should not supplicate, for Allah is the Possessor of great bounty, and His mercy encompasses all things. It is not far-fetched for Allah to respond to one who supplicates to Him with sincerity, brokenness, and humility. Abandoning disobedience is easy for whoever seeks Allah's help, and He, glory be to Him, promised guidance to whoever strives against their self for His sake. Strive against your self in abandoning disobedience, be truthful with your Lord, and do not despair of Allah's mercy, for the door of repentance is open. The most important thing you should supplicate for is that Allah helps you against your self that inclines to evil, inspires you with your rectitude, and protects you from the evil of your self. The one who seeks such help along with sincere striving will not be disappointed.