I have not read any other replys, since I wanted to think through this first. Let's see how I do.

Exercise 1: Preflop, it folds to the small blind who had 15bb before he posted the blind and you have him covered. He open shoves {22+, K2+, A2+, QT+, JT}. What hands can you call with profitably in the big blind?
With such a wide range, we could call with 22+, Ax, Kxs and it be profitable. Add in Kxo, and we're just better than a coin flip.

Exercise 2: Preflop, a 20bb stack opens for 5x with {AQ+, 99+} UTG. You call on the button with A K and you have him covered. The flop pot is 11bb after the rake and you have 15bb behind. The flop comes AQTr. Villain open shoves 100% of his range. Can you call profitably?
We have 55% equity against his range on this flop with TPTK. We're calling 15bb into a 26bb pot, which is giving us pot odds of 57%. We still have outs on the turn/river with any K. We can call profitably here.

Exercise 3: Preflop, it folds to you on the button. Both blinds had 20bb stacks before posting the blinds and you have them covered. You open raise to 4x, the SB shoves {AT+, 22+}, then the BB shoves {AQ+, 88}. What is your profitable calling range?
We have a nitty op2, but we can have a wider range and be profitable here since it's three way. Let's say 35% will get the job done. 55+, AJ+ should be profitable here.