I'm almost always happy to get it all in with AK preflop, but as always it depends. Are you pushing against multiple opponents? Do they have a wide 3 betting range or a small 3 betting range? What are effective stack sizes?
1.
As a rule of thumb I 4-bet 3x the intial 3-betters amount so if you're buying in deep and topping off your stack this isn't a shove. With this sizing you'll still get folds from marginal 3-bet holdings while risking the minimum.
2.
Again depends on your opponents 4-betting range, and the pot
odds being offered. After typical online open and 3-bet sizings you'll need about 45%
equity to make the call. (bbs in pot before shove = 1,5 + 3 + 9). If he's shoving tight (JJ+, AKs, AKo) you'll have 40% equity so you're supposed to fold. If he has reason to suspect you're 3-betting light (e.g. 3bet from the sb to a button open) he might also be 4-betting a wider range which makes this an easy call. (against 88+, ATs+, AJo, KQs, AK has about 51% equity). Since you're unlikely to face a 4-bet shove when playing sufficiently deep you'll almost always get the odds to call or 5-bet shove with AK.