For the first question. The responders will act exactly as if there is no DNR until you give it to them. Yes, that sometimes means wasted effort but it's better than the alternative.

For your second question, by legitimate I basically just mean that it's not written in crayon on a piece of notebook paper or something. Generally speaking the forms are pretty standard and issued by the healthcare provider. Generally you're just looking for a physicians signature and a date. Some states also allow DNR medical jewelry. The exact specifics on the DNR do vary a lot based on state and county so the local responders will know what they need for their area. As far as every second counting goes, that's why you have a whole ambulance crew.