Question 1:
No the "top of the decK' doesn't go to the bottom just because it's flipped around. A feather of the phoenix will place that card right on top face-up. Top of the deck is determined by the current position of the deck, if you get what I mean.
Question 2:
I believe that this will cause you to lose the match since you got no more cards to draw. If Card Destruction is "pick up" then what you say is true, but now it's draw.