Family

Bismihi ta'ala

As the holy verse in the Quran says God's mercy encompasses all. You can ask the Almighty to show His mercy upon them, and overlook their shortcomings, etc. 

Unfortunately some Muslim groups believe it is haram to prayfor a non-Muslim in any way, but reality is such an approach is difficult for one whose family might not have recognised Islam and be good people. 

Just requesting Almighty God to show His mercy would hopefully assist them in their next life. 

And Allah knows best.   

Bismihi ta'ala

This is unacceptable. Whatever the family's religion may be, Muslims must honour and respect their families. Your wife has no right to do this. 

If she has certain concerns, you should address them. There might be something she has seen, like abuse, or intimidation, or trying to brainwash your son, etc... Try to pinpoint what the dispute is about, and deal with it. 

But if it is just because she has no respect for your family, this does not give her the right to deprive her son of visiting or being with his grandparents and family. 

With prayers for your success.  

Bismihi ta'ala

If all other shar'i requirements are met, yes, she can marry that man.

The marriage proposal must take its normal procedure, primarily around the parents giving their consent and their blessings. This is the most important part. 

A second important step is to see the character traits of the person, their moral standards, their family, compatibility, etc.

A third step to take is seeking consultation and advice, trying to find out if this prospect marriage is a good idea, and the obstacles they might face. This is necessary for any case of marriage, Muslim born, or convert. 

Both of them should study this from all its angles, for the sake of making the right decision and having a successful marriage. 

With prayers for your success.