Hand 1 I call...AT seems like his most likely holding.

Hand 2 needs reads...both approximate 3b frequency and overall skill level. I dont think we can assume he will know you raise most fl draws otf. I'd lean towards checking back...we can win occasionally vs his broadway fl draws and I doubt he will fold 89 type hands.

Hand 1 i think not many 7's play this way and/or 3 bet pre, AK/AQ would probably lead flop and almost certanly raise by the turn and would he really call QK on the turn ? TT might play it this way but again i am not sure he would flat the turn and JJ would probably raise on the turn also. His most likely hand here is AT or some spazzy Ace trying to get you off what he perceives as a chop. Did suits matter at all was there a backdoor flushdraw that missed on the river ? I am calling though.

Hand 2 as above need more info but i would say that he ' might ' play some mid pairs/TT like this and that his call on the turn indicates he might well be sticking around for the river, yes you might get most flush draws to fold but you also win against some of those by checking back. It does seem like a check though.

Hand one I agree with Steven. I'd definitely call. Occasionally run into KQ. But he can be betting worse for value hands like AT, AK,AQ. We block the top of his value range of AA and JJ. I think there are more combos of worse value hands and some air balls like small pocket pairs or maybe KJ he's turning into a bluff than there are actual value hands. 

Hand two need more info about villain. I'd love to jam but what can we get a fold from and what are we repping  when jam here? What value hands would we jam here that make sense?

Luke, kind of off topic, but is 2.5 your standard raise size from LP?  You're a wizard, so I'd love to know the rationale.  Get more folds/bloat the pot IP =get you more turn folds than minraising?

HAND 1:  rainbow board?  if so I really think AQ/AK are value owning themselves, or A7  miraculously flopped the world.  I also can't imagine folding river when you have underrepped your hand so well.

HAND 2: being slightly more shallow, i might(maybe very poorly) 4 bet fold here.  Sucks turning our hand into a bluff here, but saves us guesswork on future streets.  We have an ace blocker, so his 5bet range should be much stronger, most of the time.

as played, i'm sigh checking back, as we just arent repping enough value hands even though river is prob a very good card to do it with

Ok,

A few thoughts, 

Hand 1,

I think its a fold, I did call, but I think its a fold, I'm going to explain why, when villain takes this line I think he's almost always value betting, I think he has to be concerned that AK/AQ are not the best hand, to me his line looks like something that slow played the flop, or maybe JJ/TT/KQ. Even if he does AT, vs a range of AT, 7x, KQ, JJ, TT, AJ, AA we aren't looking to hot. I also think AJ and AT are kind of unlikely to be his hand because i wouldn't expect him to 3bet those. I really think this is a fold and in game I tanked for 2 minutes and ended up calling and losing to 97o.

Hand 2, 

I think we rep any set, straight, two pair, which are all hands we can play like this. As for pf I def can't 4bet fold, if I'm going to 4bet I'm going to 4bet call. Anyways I think this one is kind of close, if the flush fills obviously I need to bet, I think this specific river is probably good for his range, it seems as if he's likely to have middle cards, and the river is a middle card so I think sigh check back may be the play here, I shoved here and ran into a straight with some junky hand i.e. 67o.

Lucas,

Hand 1: I think the river decision basically comes down to this. Since his line here is kind of unorthodox when c/c c/c openjam on that board there is basically two things going on:
He either slowplays a monster (a hand that clearly beats AJ) or decides to turn his hand into a bluff OTR. I think about this way.
I'm guessing in a 700 progressive KO tourney, the level of play is higher than in really large MMT fields with smaller buyins where people are spewing from left to right. His 3b sizing seems in line of a reg who knows what he's doing. I don't see why AJ/AT wouldn't be in his 3b range SBvsBTN if the previous assumptions are correct. I also think it's pretty unlikely he plays KQ/AT this way aswell. (KQ bets at some point rather then c/c and AT usually checks river). If villain were to turn something into a bluff i'm thinking KK/QQ are good candidates for that and some Ax.  The weaker i think the player is, the more likely i think he turns hands into bluffs and "panics" like some weaker players do and just spazzshove river. Since i think he has some idea of what he's doing with the very little information we got i think this is more a fold than a call. Also, with the potodds he's giving you on a call this sways it further.