#1 - Holding a gold coin in your hand, continual light is cast upon it, and it glows light. Then invisibility is cast upon the coin.....can the light still be seen?
My 2e books are downstairs in a box so I don't have a reference, but I would look for examples of a torch having invisibility cast on it. If the fire from the torch would be seen, then the light from the coin would be seen as well. If the fire is invisible, then so is the coin. Assuming the lack of any other examples of a light source (rather than reflected light) being the subject of an invisibility spell I would rule that no, the light from the coin is not visible.
#2 - Continual light is cast upon a bowl of water, the water is then drunk.....when the person pees, will the water exiting glow?
No. When you drink a healing potion, does your pee retain healing properties? I'd rule that magic passing through a living body loses its magical properties. If a DM rules yes to this, then she has to think about where else the water goes in the body. Water's used for a lot of things in biology, not just urine. The person's sweat might glow, and theoretically the cytoplasm of the cells might also glow. Too much mixing of science with magic for my tastes. The solution is simply, no, it doesn't.
#3 - Invisibility is cast on a person, who then drinks the water from #2.....can the water be seen going through the person's body?
No. When a person who is invisible picks up an object, the object becomes invisible as well. Thus, water that is drunk becomes invisible. Of course, this depends on the answers to numbers 1 and 2. If continual light objects within an invisibility spell are visible, then the water would be visible. However, it would only be visible for a certain distance into the digestive system because of my answer to number 2. If the DM rules that continually lit water will glow after leaving a person's body, then the water will be visible for its entire passage. But then you face the same questions of where exactly the water goes.
Doc: I'm a pacifist. Caboose: You're a thing that babies suck on? Tucker: No dude, that's a pedophile.