Does seeing the Prophet, peace be upon him, and Umar ibn al-Khattab, may Allah be pleased with him, in a dream, smiling, signify guidance and the abandonment of sins, especially considering being afflicted with the sin of sodomy and not maintaining regular prayer?

Sodomy is a grave indecency, and abandoning prayer entirely is disbelief. Seeing the Prophet (peace be upon him) in a dream is a true vision, and Satan cannot impersonate him. This dream may indicate Allah's care for you and His desire for good for you. Hasten to repent to Allah and do not despair of His mercy. The one who repents from sin is like one who has no sin.