Cashes have come back and I'm playing !!, plus a hand and a dry pot

I played 4 tournaments this Sunday and cashed in 2 of them (a $200 and a $100), even the $200 was a little disappointing, I finished 63 out of more than 2000, I'm happy, not for the cashes but because I'm playing more and more and that's good. There were many interesting hands yesterday, one I remember from the $100+9 was the following:

We were already in the money with 4 tables left:

PokerStars No-Limit Hold'em Tourney, Big Blind is t1000 (9 handed)

saw flop|saw showdown

BB (t27883)
UTG (t3198)
UTG+1 (t10865)
MP1 (t42597)
MP2 (t36125)
MP3 (t11358)
CO (t16250)
Button (t25556)
SB (t23607)

Preflop: Hero is SB with Ks, 5s.


UTG raises to t3098, 5 folds, Button calls t3098, Hero calls t2598, BB calls t2098.

Maybe the call was in the loose side, but I did it because of the all in guy, we have a good dry pot and usually this means people let you see more cards while you don't let them if you hit or think you can beat the all in guy, in this case I have to hit

Flop: (t11692) Kh, 8c, 7s (4 players)

Ok, I hit and I'm first to act with 2 guys in the pot besides the AI guy, I decided to bet to isolate, but I thought a small bet was enough to get rid of players with an ace or an small pair, and if I encounter any resistance (a raise) I just fold, since usually a raise in a dry pot situation means a hand

SB bets t3000, BB raises to t24685, Button folds, Hero folds.

BB went AI after my bet, he had been playing pretty tight up to that point, I was prepared to fold but still took a moment to think about the chance he had something like A8 and wanted to really isolate, based on his play before and the fact that he was doing that versus a bet and a guy still to act made me fold

Turn: (t39377) Tc (2 players)
River: (t39377) 8s (2 players)

Final Pot: t17692
Main Pot: t17692 (t17692), returned to BB.

Results in white below:

BB has 9c Th (two pair, tens and eights).
UTG has Js Ah (one pair, eights).
Outcome: BB wins t17692.

I was debating the BB play with a friend and I think the fold was the correct play here and I don't like much BB's play (even it worked for him, THIS time). What do you think?

AK and a short-medium stack

Another mistake I think I use to make a lot, it's when I have AK, let's say on MP with a 10-17x stack, the stack may be too big to go all in, but if I make the usual raise to 3x and got called by somebody on the button for example. I have a hard time playing the flop, the pot has about 8x and you have 7x-14x left. Lets say 3 rags come, my mistake is I go all in a little too much in this situation just to be called by any pair, so, there must be a better way to play the AK here, shove preflop?, check-fold flop, mini-scare bet flop?, and of course I'm assuming you know nothing about your opponent.
What to do?, please do tell me, I play very bad the AK missed flop, I should say in general, but specially when I don't have a big stack.