The point of the fork in the hot dog is to hold the hot dogs under the water so that the end of the hot dogs don’t get over cooked by being out of the water and getting direct exposure to microwaves (which most hot dogs will do since they will float in the water). No, putting a metal fork in the microwave will not hurt your microwave. If the fork touches the side of a running microwave it may spark and damage the fork or the metal shell of the microwave, but as long as you prevent this it is perfectly safe.
Grasp the fork with a hot pad to take out all the hotdogs.