Positive vs negative, power vs ground, flow direction
(This comes up frequently; have you checked other questions on the definition of voltage?)

The key to understanding current is that it flows in loops. Power transmission is like a chain drive on bicycle. It's distracting to think of it "coming from" either of the terminals. Power is delivered by the current flow past a point.

Thinking about electrons is nearly always a distraction unless you're looking at semiconductors. As it happens, you're correct in (3): electrons flow from - to +.

The answer to your (1) is "yes" and your (2) is "question makes no sense".