Depends on your state but most likely yes
In Australia, depending on specific court orders, yes, but usually a good reason is needed. ("not wanting to" is NOT considered a good reason!)
nosee links
No there is no need for the child to go to Texas.
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.
can noncustodial parent parent claim 1 child if divorce with 2 kids
A child may not decide until he is 18yo.
no
You need parental consent to move until you are 18.
if the child doesn't want to see the noncustodial parent he doesn't have too. don't force him to do it =)
Generally, no.
no
Child support in Ohio usually continues until the child is 18, and up to the age of 21 if the child is in school. Whether or not you have to pay child support if the child is living with the noncustodial parent depends on the support order that it is in place Typically you can expect that you will have to expect to pay support.
The one who would be responsible for the child during that time which would be the non custodial parent.