Is "De" pronounced the same as "Day"?
No but in Nynorsk and in several dialects it "dei", pronounced like eng "day" instead of de. So it is possible that you have heard a Norwegian say "dei".
No, it's pronounced like the English word "me", but with a D-sound instead of an M-sound.
It's pronounced as an English person would pronounce "Dee"
It's not pronounced like English at all. It's the best to listen to the examples, and base it on that. Don't base it on another language. It'll confuse you if you do that.
Why is "You like us" (as in the formal you) wrong?
I don't think the formal you (singular) as De is taught in this course at all, as it's archaic & very rarely used.