yes
If both of the parents have a joint legal custody arrangement, you have to give the noncustodial parent that information. If you have sole custody of the child, you do not have to share that information with the noncustodial parent.
No
Yes, being granted full custody does not relieve the other parent of their financial obligations to the child(ren).
If the noncustodial parent tries to keep the child, the custodial parent can get the noncustodial parent charged with kidnapping and contempt of court both can be jail time for the noncustodial.
Not as long as it doesn't interfere with the access rights.
Usually, yes; however, some parents with joint custody pay support.
can noncustodial parent parent claim 1 child if divorce with 2 kids
Not without a a first right of refusal in the current custody orders, or custody modification
That is up to the interpretation of the courts and why the arrears exist.
No you are not. It is the noncustodial parent's responsibility to make arrangements to visit the child. All this should be included in your custody papers.
Alimony to the non-custodial parent may still be ordered; depends on the circumstances. Child support payments are based on both the needs of the child and the ability of the parent to provide them.