Again, it's not a problem from the Energy standpoint but I always felt like the use of the word "light" implied visible photons bouncing through the core of the sun to the surface, which isn't really the case as far as I can see. One of those terminology issues I always got told off for!

True on the Energy for sure, although the photons would still be coming if fusion stopped! White dwarves have no fusion occuring but still emit photons, and take Trillions of years to cool to black dwarves that are too cold to emit light.

The origin of the Energy is for sure the core, and the gamma rays produced there and reabsorbed spread that energy out pretty well, but the visible photons I believe are mostly from the material in the Photosphere as that is at the correct temperature for the black body spectrum we see.

It's a great fact, but my only issue with it is that the vast majority of the light we see is emitted by the Photosphere of the Sun, not the core, so it sometimes gives the wrong impression. The Sun is mostly just a Big Hot Thing in space!

Light is slowed in mediums it iteracts with - we call the phenomenon Refraction and it's how Lenses work. In stars, the plasma is incredibly hot and dense, and loves to interact with the EM fields that make up light waves, hence the big slow down.