1.) maybe the Gaster Blaster is named after Sans using it against Doctor Gaster when Papyrus is injured or when the doctor seriously peeves off Sans during experiments
2.) The Blue Heart attack that Gaster uses on Sans and Papyrus seems to be the same one that Sans uses on Chara/Frisk during the Genocide run. Perhaps Sans learns to use it by watching Gaster use this magic attack.
3.) maybe Sans can reset and teleport because he is the one who threw Gaster into the Core's center. Accident or not, that's why he is so strong and able to do such powerful magic. This might have given him a little bit of a Level of Violence, which is countered on