A Designated Router (DR) is elected among the OSPF routers in a network to reduce the overhead by acting as a central point for exchanging routing information. The election process follows the rules defined by the OSPF protocol, meaning there must be a negotiation to determine the DR. Only NBMA (Non-Broadcast Multi-Access) or Broadcast networks need to elect a DR; other types of networks like Point-to-Point or Point-to-Multipoint do not require a DR. Therefore, the statements about the DR being elected among the routers through OSPF protocol negotiations, and that only NBMA or Broadcast networks need a DR, are correct.