fold equity has nothing to do with you folding, it's the likelihood that your opponents will fold to your bet.
So if a player has 1,000 chips left and 800 of those are in the BB...what are the chances he will fold to your button raise? pretty much slim to none...so in this case your fold equity is almost zero.
as for stealing the blinds..
I think, as with many things, stack size determines which moves are in our arsenal and which are not. Which are most profitable and which should be reserved for different situations. Certainly with 80bbs, open shoving preflop should NOT be in your arsenal. certainly with 8bb open raising should not be in your arsenal.
In the situations you described ~10bb and it folds to your button...I wouldn't shove any 2 here, but I'd shove probably the top 60-70% of hands (which if you look at a hand rankings
chart will appear almost like any 2 and includes such beauties as T2s and 96o...couple that with some fold equity and its ok to shove pretty wide on your button.
with a 20bb stack, I think it's too big for an open shove but the PERFECT size for a re-steal. so look for somebody who is raising light, pick a hand with reasonable equity if you get called (unlikely to be dominated...so I'd rather resteal with T7 than A7) and shove.
with a 20bb stack open raising is in your arsenal, but it is VERY trick indeed. if you want to raise a hand, raise for value...so from early position pick a hand that can stand up to a re-raise and from late position pick a hand that you won't mind being all in if you catch a piece of the flop.