To answer your 2nd question, you can certainly add butter to your tea. In fact, in the Himalayas the locals drink yak's butter tea. I've found unsalted is better ;-)
Didn't really like it with coconut oil though.
I don't know the science behind the bulletproof coffee, but we are naturally generally in a ketotic state when we wake after fasting all night, so having fat first thing would fuel that state. Especially the medium chain triglycerides in the coconut oil, which are readily used to produce ketones iirc.