Is it permissible to marry a man who used to commit fornication and had multiple sexual relationships, and who openly expresses his desire for all sexual practices, and has liberal views regarding his wife's appearance, knowing that he prays and claims to be a Muslim? And is this considered a punishment from Allah?

If what was mentioned about the man is true, then it is not permissible to marry him because he is not satisfactory in his religion and character. A fornicator is not a suitable match for a chaste woman, and it is not permissible for him to marry her, as Allah Almighty says: "The fornicator does not marry except a [female] fornicator or a polytheist, and no one marries [a female] fornicator except a fornicator or a polytheist, and that has been forbidden to the believers."

He is a stranger to her, so it is not permissible to talk to him except out of necessity, or to allow him to touch or kiss her. The relationship with him must be severed. Love sickness is an ailment that can be treated with patience, fasting, occupying oneself with what is beneficial, keeping company with righteous women, and avoiding everything that incites desire.

Shortcomings in worship may be due to sins. One must repent, conceal the sin, and resort to Allah with supplication for Him to grant her a righteous husband.