A Cup of Tea

Bengt is back from his winter holiday, and he's exhausted. So he sits down by the fireplace with a nice cup of tea. The cup is cylindrical, at least on the inside, with radius r and height h. He has three footstools; first he had two, because he figured he has two feet, but then he added another to put his cup of tea on. The stool-tops are horizontal - Bengt's woodworking skills are dubious, but he didn't make these. As the tea stands on the stool, the depth of the tea is d. Then he picks up the cup, and tilts it towards him, as people tend to do when drinking.

1. At what angle is the bottom no longer covered by tea?
2. At what angle does the tea reach the top of the mug, and thus Bengt's mouth?
3. Come to think of it, Bengt is curious about how fire works. It emits light, that's plain to see. But is that light just black body radiation, or is it some sort of chemical process that emits light in itself?