NO!
Yes, it can. Moving in with the other parent is grounds for "flipping" child support payments. However, this must be done by court order.
No there is no need for the child to go to Texas.
see link
When they move out of the custodial parent's home see links
Whose name is the phone in?
The noncustodial parent is only responsible for any child support payment. It is the responsibility of the custodial parent to organise the child's life, including any necessary insurance cover. Basically, you didn't want them having any say in the child's life, so you cannot expect them to simply do everything for nothing.
Well if the noncustodial parent wishes to take the kid the judge might give the parent custody if there is not a bad reason the parent did not get custody in the first place hope I helped you
With court approval and provided welfare is not involved. see links
Too complicated to answer simply. See an attorney that does child custody and family law.
yes
No the new spouse is not responsible.