What is the ruling on a father's behavior who talks to girls via "Facebook" and refuses to pray in the mosque, citing knee pain as an excuse, and is it considered spying if his children remove the girls from his page, and does the father's role as a role model get affected by these actions?

What the father did by talking to foreign women and having their pictures is a reprehensible act (munkar), and the son's looking at his father's computer without his permission is considered forbidden espionage. The obligation of congregational prayer is a matter of fatwa, and the son should advise his father regarding it. It is not forbidden for the son to no longer feel towards his father as he did before, for a person loves and dislikes according to the amount of good and evil within them. The son must honor his father, even if he is disobedient, and among the greatest acts of honor is to denounce the reprehensible act with kind words and advice.