) what right the family has to stop/prevent him doing any acts against the welfare of family/ children.
Nobody can legally stop him from indulging into any such illegal act or undesirable act, but can give complaints against him for his unruly behavior and assaults if any with the police and refusal to maintain the family seeking maintenance through court of law.
2) if he really has/gets no. of illegitimate children, what is the fate of present legitimate children
There is no answer for this. Even if he is into an illicit relationship with any other female other than his wife the children born out of such relation are not called illegitimate, they are his biological and legitimate children.
3) can the minor children has any property rights
They do not have any rights in his self acquired property
4) Can the family stop him to do any property transactions
His wife can file an injunction sit restraining him from selling his property in order to create charge on it for his failure to maintain them or give money for their maintenance or sustenance.