No, a flush beats 2 pair. There are 10 ranking hands, in descending order: Royal flush, Straight flush, 4 of a kind, Full House, Flush, Straight, 3 of a kind, 2 pair, 1 pair and a no pair hand.
No, it does not.
The hand rankings from lowest to highest are:
High card A pair Two pair Three of a kind Straight Flush Full house Straight flush Royal flush