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Hand 1.
Having 1:7 I whould buy a free card here, and may be would force UTG to fold such hands as AJ and AT or KQ.
But it is a blind response, reads in this case are crucial.

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So it makes sense to raise the AK when you are going for a free card?

How would the read alter the decision?

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Sometimes, yes. Lots of players bets automatically on preflop raiser on such flop when heads-up and fold to raise.
The second option is to see the turn (but only if the player is passive). When their bluff on flop fails weak/passive usually give up on turn and your bet may win the pot.
No free cards with LAG! He may face you with the 3-d raise. Just call him down.