How can a planet not rotate at all and yet have 1 year that is day and 1 year that is night?

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...