I recently watched an episode of Supernatural - the episode references Western themed movies as well as the image of two men with their hands ready to fire on each other.
Did duels like this actually happen?
Why did they wait to pull their gun out? I did some like googling and a somewhat sketchy website said people can do actions faster when reacting instead of simply doing it.
So did they wait so they could react to the other person?
I think one of the Presidents, and VPs had a duel - is this how the would have done it?
I haven't seen this show, but
Did duels like this actually happen?
No. From the FAQ:
How common were western movie style shoot outs and duels in the wild west?
As u/gamblekat explains above (read more here), the few times it did happen became enshrined in the myth of the "Wild West," so much so that pop culture just assumes it was commonplace. But events like the shootout at the O.K. Corral became famous because they were rare events. In the Luke Short-Jim Courtright gunfight both men drew pistols from their hip pockets, not low-slung holsters.
The duel you're thinking of is the duel between Alexander Hamilton and Aaron Burr, fought while Burr was sitting Vice President. This would have been a different type of duel, with both participants following strict procedures before facing each other and shooting.