If non custodial parent quits one job and gets another job and custodial parent has not received a child support payment in a month will custodial parent get child support again ?

Yes. The missed month becomes arrears and gets charged interest. If this were to happen, and the custodial party knows where the non-custodial parent is working, the custodial part can help speed up the process by calling their local office and reporting who the new employer is.

Yes as long if the order is still in place. Non custodial will pay child support until the order ends.

Once a court is established the the amount ordered is expected to be paid every month until the child emancipates.