If the custodial parent left the state and gave the care of the child to a non-family member is the noncustodial parent still obligated to make support payment?

Is the parent planning to come back and yes...you would still have to pay...or take it to court

How can the non-custodial parent keep in touch with the child during their separation? Please advise on what steps can be taken to keep in touch no matter of the custodial parents transitions?

Yes... support remains due. Call the office to advise them of your current situation

Yes