How can a planet not rotate at all and yet have 1 year that is day and 1 year that is night? A mercury day if you consider its solar day is 2 mercury years.

Now if you consider just 1 half of mercury, in 1 of those years it is facing towards the sun and in another one of those years it is facing away from the sun.

Mercury is tidally locked. This tidal locking happens when the rotation rate slows down until it reaches 0.

How is it possible for a planet to not rotate and yet have 1 half of it facing towards the sun each year with that half changing every year? It would seem like it would have to rotate 180 degrees in a fraction of a second which I know is not possible.
Your premise is incorrect. We used to think Mercury was tidally locked, but since 1965 we now know it is in a 3:2 spin-orbit resonance, which gives it (long) days.

Anything you read that says it is tidally locked is old, or itself using old reference material.

Here are some quick sketches to show the orbit, relative orientation of the planet, and the sidereal and solar days. If you like it as an answer I'll redraw with a graphics tool instead of my iPad Pen app...