How can I return to prayer and my previous commitment, and will Allah accept me after my repentance from adultery, knowing that I feel extreme guilt and that I do not deserve to live?

The feeling of remorse over a sin is a sign of good and an indication of the heart's rectitude. It is also one of the greatest pillars of sincere repentance. However, it should be a motivation to draw closer to Allah and strive in good deeds, not a deterrent from good. One must beware of despair and succumbing to the whispers of Satan, for Allah accepts the repentance of a servant no matter how great their sin, and repentance erases what preceded it, and "The one who repents from a sin is like one who has no sin." Among the signs of sincere repentance are avoiding the causes of sin and places of temptation, and striving to improve one's acts of worship. Among the things that help with this are: correcting one's intention, focusing on the actions of the heart, striving for righteous companionship, avoiding bad company, frequently remembering death, contemplating the signs of Allah, along with persistent supplication.