Stay out of the issue. His girlfriend is your ex's problem, not yours. She has no right to interfere with child visitation or trying to stop your child from staying with his father. If she's trying to intrude on your child's visitation (or your ex seeing his child) then your ex needs to deal with this on his own.
However, it's to be expected that anyone who dates your ex (and anyone who dates you) would be upset if you're spending time alone visting each other, when it's not due to child visitation or discussions about your child. It's a good thing for two parents to stay amicable towards each other for their child's sake; it's another matter if either person still has an attachment to the ex and is trying to renew an emotional or sexual relationship. You can't expect his girlfriend or your boyfriend to tolerate that.
Don't be around her when her father is around. Hang out after school, etc. Just don't go over to her house.
The parents of the deceased father (the childs grandparents) can do a paternity test.
No
Yes, he can, just as any parent is entitled to do so around their children of any age.
Yes
A girlfriend may not want to introduce her boyfriend to her father, because they do not get along. The girl may also be embarrassed of her boyfriend or father.
If your father and your girlfriend's father are second cousins, then you and your girlfriend are third cousins. You share one or two great-great-grandparents.
The childs' father, married or not. Your relationship to the father is irrelevent. The father is the first on a long list of family members. Create a living will if that is not acceptable.
alone, because say if her sister mother or father is saying no trying to put her of?
You can, but eventually the court will question what you are doing.
It isn't the birth father, no one will ever change the childs birth father, but he will legally be the step father,until the divorce comes through.
A childs mother must file a petition for child support in the local family court.