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Both cases you give are calls imho. The main factors to consider are the bubble factor (or ICM), stack sizes and the pusher's range.
As you probably know, with 4 players you are on the bubble and so you need to get your money in when you are pretty likely to be well ahead. So in case 2, if he is just pushing 99+, AQ+ then AK is about 50/50 to win, but you would have to fold because that's not nearly a good enough edge. In fact according to SNG Wiz - a program that has a free trial that you might like to at least investigate - he has to be pushing at least 17% of his hands for this to be a call. All except the very clueless or terminally nitty will be shoving at least that wide in the small blind in my opinion, so I would call.
However, if your friend had a much bigger stack, say 6000 too, then he would have been correct to fold AK. Big stack v big stack means a huge bubble factor and even if the small blind was shoving any 2 cards, it is still unprofitable to call with AK, according to Wiz. This is fairly intuitive. As your friend found out, AK is at best about 65% to win against any two live cards and so calling means a 35% chance that you get eliminated and the 2.5K stacks get their hands on the prize money you had a good chance of winning.
As it was though, in both cases you had the smallest or almost the smallest stack, so you need less of an edge. In case 1, the shortest stack is shoving on you. If you fold he overtakes you in chips. You only have 6BB, so you are under some pressure to act. You have AK, so its pretty likely you will be at least a coin flip against him and you could be well ahead. Its not a brilliant spot, but its likely to be the best you will see for a while. So call and if the worst happens, you will still have a few chips. In fact if the button is shoving 10% of his hands, (which would be a very conservative range for a loosish player with 5BBs on the BTN), WIz has 99+, AQ+ as profitable in this spot.
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