Question on how to use equity calculation vs EV vs ICM to evaluate a home tourney

I am new to using an equity calculator to evaluate my game once I get home from playing, and I am not sure if I am doing it right. I am sure this will seem elementary to most of you, but what I like about tournamentpokeredge is that people are helpful as opposed to other sites where I would be ridiculed for this question.

Here is an example

Final table of $30 buy-in tourney (19 players now down to 10)
Payouts 50%/25%/15%/10%
Blinds 500/1000/200

Average chips ~12,450

UTG (villain) has me covered
Hero 11,200 chips
Next five people to act have 4-7 BB’s
CO Chip leader
SB average type stack
BB slightly above average stack

First hand after the break and we are just moved to the final table. I have been playing with 3 of the shorter stacks and they are clearly waiting to try to survive and cash

3500 in the pot (blinds and antes)

UTG makes it 3000 to go and I have AdKd

I put him on QQ-99,ATs+,KTs+,QTs+,JTs,ATo+,KQo.  I am discounting AA and KK since I have blockers

If I shove and I am called I am risking 11,200 to win 25,900 (including my bet and his call)
( I could also win outright if he folds)
I am also assuming that the CO/SB/BB will fold since UTG can go all in, my bet represents a large portion of their stack, and there is no reason to get crippled with so many short stacks they can bully or wait out. I think the short stacks will wait for a better spot.

Here is where I get confused
My equity calculator (that I just used for the first time) says I have 60% equity against his range.
I. Do I use the 11,200 (my bet)/25,900 (with my bet, the pot, and his call) =43% to evaluate this shove
Does this make the shove mathematically correct since I have 60% equity?

2.  Or do I just use EV and say that 60% I win 25,900 (8820) and 40% I lose 11,200 (-4480) for a +EV of 4340?
Does this make the shove mathematically correct (or am I just saying the same thing twice)?

3.  Does ICM change all of this? 

I not happy about just calling because If I just call with ~25% of my chips and villain C-bets on a flop that I miss, I may have to fold with only 8BB’s left (and 200 chip antes for a Q of 4), Also this is too strong a hand to fold pre-flop. So a shove seems like the best play.  Does anyone believe that people are less likely to want to be crippled on the first hand of the final table after returning from a break?

Just FYI, everyone folded to the villain who tanked/called with AQo and hit a queen on the flop. The result is not important. I am trying to learn to use the equity calculator so I can change villain's ranges and see when I should call/shove/fold. Any constructive criticism or explanations are welcome.