NNokey,

Texas Holdem takes into consideration the best 5 cards.

So, yes you absolutely do count the second pair, and if both players have the same two pairs, then you would go down to the 5th card kicker.

Same goes for a flush, you would consider all 5 cards, with the higher cards winning the hand.

With your final scenario, it would be a split pot, because both players have the identical 5 card hand.

Hope that helps!