What is the path to repentance, chastity, and lawful sustenance, and how can Allah accept my repentance, and what should I do about my engagement and the stagnation that has afflicted my work, knowing that I have committed adultery several times?

Sincere repentance erases sins, and the one who repents is like one who has no sin. No punishment for it will befall him in this world or the Hereafter. As for what you complain of regarding the difficulty and impediment in marriage, it may have sensory or psychological causes. You must take the measures that remove this impediment by seeking Allah's help, consulting those with sound judgment, and referring to specialists.