I'll give some of my thoughts. These should not be viewed as the answers.
1) What range do you give in practice to the CO, SB, and BB?
This is a descriptive rather than normative question. It is not asking what people should do, but what they actually do in practice.
I think the CO is pushing about 40%, the SB 10%, and the BB 98%, but not necessarily the top 40%, 10%, and 98%. Some players will push 80% from the CO, and others will push 20%. If the weighted average is 40%, the range is a little weaker than a top 40% range.
2) What will happen to the short stacks if everyone folds to the big blind?
This is a critical question.
The CO is in extreme danger of blinding off, while this hand's SB can force him to win a showdown or bust out. If the CO wins one showdown, though, the SB will have to win two showdowns in a row.
I think there is a strong tendency for players to exaggerate how bad the CO's situation would be. I believe the CO would only be in slightly worse shape than the SB. The CO should cash well over 40% of the time. I think many players assume the CO would be in much worse shape.
Maybe it is more frustrating to post a blind all-in and bust out than to push all-in and get called. You feel powerless instead of in control. However, your bankroll will not notice the difference. If your goal is to win money, you should not pay money to tend to bust out the second way instead of the first.
3) If the CO and BTN had folded, what range should the SB push?
Since folding does not come close to guaranteeing making the money, the SB does not need to be an overwhelming favorite over a random hand to call all-in. It is more valuable to double up to 320 chips than to have 40 chips. One reason is that if the CO folds the big blind, the SB can make sure it is a 3-way pot when the CO is all-in in the big blind which greatly increases the chance of knocking out the CO. Another is that if the CO survives, it is much easier for the SB to survive hitting the blinds again with 1.33 bb than with 0.17 bb.
A trick we can use to make the Nash Calculator helpful is to change the blinds to 120/360 and advance them one spot. Then look at the EQpost calculated by the Nash Calculator. This forces the Nash calculator to see that the CO will be all-in.
If the SB folds, the Nash calculator suggests an equity of
10.99% of the prize pool.
If the SB calls and wins, the Nash calculator suggests an equity of
14.76%.
That means the SB should call with 10.99/14.76 = 74.46% equity against a random hand, or TT+.
Actually, the SB should get all-in a bit more frequently, since the big stack should shove often, and the BB can almost never call. That means the SB can call to end up with 480 chips instead of calling to get 320. That would give a different fraction, 11.00/16.42 = 66.99% equity against the big stack's range.
4) If the CO pushes, and the BTN and SB fold, what range should the BB call?
The medium stack is not that risk-averse. Beyond what the ICM says, the second stack would usually like to end the bubble to stop giving up so many blinds to the big stack. If you put the CO on a range wide enough to include AK, then the BB can call ATC getting 6:1. There are times to fold when you are getting 6:1 odds, but this is not one of them.
5) If the CO pushes, and the BTN folds, what range should the SB call?
The SB should expect the BB to overcall very often. Therefore, if the SB calls, he needs to win the main pot or else bubble out. The CO can lose and not bubble out, either by winning the side pot to stay alive, or by placing third if the BB wins. This is a huge disadvantage for the SB, and it means the SB needs a large amount of equity to call.
If we put the CO on a 40% range, then the CO is about a 60:40 favorite over the big blind. Folding is worth about 20% when the CO busts out, and about 1% if the CO wins, for an average just under 9% of the prize pool.
Calling and winning the main pot is worth about 16% of the prize pool. So, you need about 9/16 ~ 56% equity in the 3-way pot to call. Only QQ+ has that much. Oddly, if we tighten the CO's range, then we can't count on the BB to beat the CO as often and a hand like TT may become a call.
6) How would these change if the CO had 500 chips instead of 360?
If the CO had 500 chips, then pushing would show a lot more strength since the alternative of hitting the blinds would be better. The SB would not need as much equity to complete, but would still need a lot of equity to call a CO shove.
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actually a spot where folding aa wouldnt be the worst.
