As I understand it the kids were running it. Presumably especially Eric, since that seemed to be his special niche.
Outwardly it looks like they played a little hard and fast with the rules. Unfortunate considering that they were in it to give away money, not underhandedly rake it in.
Like good nazis, the left believes in collective punishment, and attacking the families of people who disagree with them. It is all about asserting control.
Because they want to destroy the family.
Because they were board members of the Trump Foundation. I think Donald and Eric have their own charitable organizations which are separate from the Trump Foundation. I don't know how this impacts them.