K4o check call flop because he felt like, check call turn because he has a pair and check river. Hence hero shouldve valued bet him.
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Q♦:Q♠: he might think slowplaying is a profitable play in this spot and he never goes for value . Its an often made mistake weak players do
Given the fact that he's a fish, he has a wide calling range. I think in this spot he has 33. :f_ugly::f_ugly::f_ugly::f_ugly:
I think he had 53o, since he called both turn and river and the hero is surprised it's because he is beaten, indeed he wouldnt be surprised if his ten high holds, i think the vilain tried to make him bet the river again since he had bet both streets.
Fortunatly form him the hero didn't continue his agression and walked away with minimum losses.
AA, due to the fact, that you were "very surprised to see that hand". Since even what we call a calling station fish does not have 100% but a slightly lower vpip, its nearly impossible to guess the bottom of the range (and be surprised to see him calling with a very bad hand like 32o) and even very passive and bad players may raise once in a while, when they get the nuts (89). Due to the possible straight on the flop, villain probably will not raise a set, but there are more combinations of AA then of any sets.
My guess: 10-2.
The BB is a fishy calling station.
Fish have one very specific trait - when they hit a top pair, they stick to it - no matter the kicker, no matter the board.
They just think their top pair is Master of the Universe.
I think BB had 10-2 - because it is really a surprise how anyone would call a raise with such a crappy hand.
And it is also a big surprise for Hero, because despite his better kicker, he cannot win against the 10-2, because of the higher cards on the board.
It is a surprising split pot in the end.
T♠:T♣:
that's my read because he was fishing him, and he was afraid to raise because the board is showing possible straight hand.
As we were very surprised, villain doesnt have any 10,7,6, he had no 2 overcards, oesd or gutshot on the flop. He will neither have 88-99 So, his "very surprised" range is undercards, 22-77, TT-AA, maybe AK. I don't think that villain will call undercards preflop, 22-55 on flop, AK on turn. So its 66,77,TT-AA and from here its guessing. I think the most surprise hand is AA.
If it is so nearly imposible to guess, then I think it is 32. It is the only hand that doesnt connect with this board at all. It is not paired and on the flop Villain needs 4 and 5 on turn and river, to hit his something 'backdoor gutshot draw' 
And he almost succeeded! 
That's what surprised hero
3♠:4♠:
Given that we (somehow) know it's a fish, this hand can definetely be in his range of preflop calls, as he already put 1BB in the pot.
He flopped a gutshot and checks in order to get a free card. He doesn't bother himself to calculate the pot odds (2/3 pot bet, so 2 to 5 for him to call, given 4 outs). He just wants to draw straight. Then he hits the 4th pair on turn, this is enough for him to check-call. Not hitting his '5' on the river, he checks again with the bottom pair. I don't see him checking if he hit straight with 3♠:5♦:, 5♣:8♦: and especially 8♣:9♥: