Before I give my thoughts on the other questions, I want to provide some calculations.
If the SB folds, and the BB pushes, how much equity does the BTN need against the BB's range to call? My program ICM Explorer does the ICM calculations for questions like this:
Fold: 4212 chips, 0.3612
Win: 9174 chips, 0.4356
Lose: 0 chips, 0.2
Tie: 4587 chips, 0.3669
Equity needed: 68.42%
Chip odds: 45.91%
Risk premium: 22.51%
The second stack has to be quite risk-averse if the SB folds. If the BTN minraises instead of limping, then he gets slightly better odds, but still needs 66.48% equity to call the push.
By contrast, if the SB calls with a wide range, then the BTN does not have to be nearly as risk-averse against a shove by the big blind. Exactly how risk-averse depends on the SB's equity against the big stack and some correlations between the winner of the main pot and the winner of the side pot.
ICM Explorer is not designed to handle multiway pots. SNG Wizard is, although it takes some work to get the right numbers out of it. Put the short stack on the button and the medium stack in the big blind, and let both the short stack and the big stack push in front of the medium stack who has posted a blind of 300. Make sure Tools->Options->Analysis->Show analysis details is set to True. (I think the default is false.) Then you can see the equities in various cases.
For example, if we give the short stack a 100% range, the big stack a 30% range, and AKo to the medium stack, then SNG Wizard reports that it is right by a lot to call, by 1.63%.
The value of folding is 35.80%. That is a weighted average of 35.1% if the short stack wins and 36.2% if the big stack knocks out the short stack.
If the medium stack's AK loses to the big stack, he has 27.4% equity since the big stack beats the short stack, too, about 75% of the time.
If the medium stack's AK beats the big stack, he has 43.3% equity. In this case, the short stack survives 28% of the time.
So, calling risks about 8.4% to gain 7.5%, and the medium stack needs about 52.8% equity against the big stack's range once the short stack is all-in. That is quite a contrast from the 68.4% if the short stack folds. AKo would be an easy call since it is far ahead of a 30% pushing range.
I believe the BTN limped with the intention of folding often if the SB folded, but calling often if the SB called and then the BB pushed.