Yes. There are two separate concepts here:
If you have a child, you have certain natural rights to see that child and participate in its rearing. These rights can be given up.
If you have a child, you have certain natural responsibilities to provide for the child. These responsibilities cannot be given up, though someone else can voluntarily assume them.
Paying child support will not cause the father to lose his parental rights - neither will not paying child support.
at times yes but usually if the noncustodial parent does want to see the child they will be denied visitation rights and not be allowed to see the child
Yes. He has rights until his rights are terminated by a court order.
In most cases the parent who has the child doesn't have to pay child support. The parent who does not have the child pays child support if they want visitation rights. In most jurisdictions, the non custodial parent must pay child support even without visitation rights.
If you are asking who pays the support for the child the 14 year old just fathered, the state will look into it and whomever the state decides to give custody will receive child support from the other parent.
no
No, as that is not a right or requirement.
If he was not married to the mother, nothing until granted them by the courts. see links
His parents pay for him and he pays child support for his baby.
If he doesn't take away visitation rights he should
Child support is court ordered. The judge decides who pays child support and how much.
The parent that pays child support does not need to pay child support for her child`s kids, only the current right parent.