Light speed is the speed limit of the universe. So if something is travelling close to the speed of light, and you give it a push, it can’t go very much faster. But you’ve given it extra energy, and that energy has to go somewhere.
If they are passing through an insulating medium that slows light down, they can actually travel faster than the light around them.
If the Sun were made of bananas, it would be just as hot
That's nice, except for that little thing called nuclear fusion. Despite the amount of potassium in bananas emitting alpha radiation smushing them together is not going to start a nuclear reaction.
Oops. I flipped my italics.
Right, there's no hydrogen, helium, beryllium, etc., in a banana as far as I know. I think your banana star would start to collapse right away and about the time it was the size of the Earth, you'd see Carbon, first, then Nitrogen and Oxygen start to fuse.
As far as the light speed thing, c only represents the speed of light in a vacuum, not in other materials. So there's no contradiction if you push some mass past 38mph, the speed of light in whatever material we're talking about. Is that what you were asking?