In a nutshell, anything to raise metabolism is good. Drinking too much water/liquids can lower your metabolism. When you have a high metabolism you feel warm, hence the statement about pee and warm hands. If you pee alot and feel cold, it is probably because you are intaking too many liquids which can make your electrolytes off balance which lowers metabolism which causes cold hands. The higher the metabolism equals being and feeling warmer. So too many liquids = more pee and lower temps/metabolism which = cold hands.
As for sugar, eating sugar raises metabolism. When you have a higher metabolism, your body functions better and that includes stronger teeth (something about calcium going into teeth when metabolism is higher – not sure though) and the ability of the body to fight off infections. Cavities are partly caused by bacteria, so if your body temp/metabolism is higher, you can kill off the bacteria more. At least I think that is part of the reasoning. I over-simplified a lot but I think that is the gist. Maybe some others can chime in to help explain.