Is a bearded man who backbites about me, boasts over me, and intentionally looks at my wife unveiled considered committed, and how should my wife and I deal with him?

Backbiting is forbidden. The Shari'a has prohibited boasting and commanded humility. It also commanded lowering the gaze and prohibited intentionally looking at a non-mahram woman without necessity. If this man has fallen into these matters, then it is obligatory to advise him and clarify the truth to him. He should not be judged as not being righteous merely because he has committed some transgressions. One should verify before accusing a Muslim. If someone tells you that he is backbiting you, then the original principle is that this informant is a slanderer, and you should not believe him. Moreover, the original principle is to have a good opinion of a Muslim and interpret his actions and sayings in the best possible way. The man may not have intended to boast by speaking about his marriage expenses, and his gaze at your wife may have been unintentional, or he may believe in the permissibility of looking at the face of a non-mahram woman without lust or fear of fitna, which is a view held by some scholars. We advise you to treat this man kindly and advise him with kindness if necessary, while keeping in mind that he is a non-mahram to your wife.