Poker Coaching: Tough Spot Against Short Stack Limp

You are eight-handed in a $320 buy-in online tournament with blinds at 50-100 with a 10 ante. Everyone folds around to the cutoff, a generally strong player, who calls for 100 out of a 1,500 chip stack.
The action then folds to you in the big blind. You look down at 7♠ 4♠ with 1,400 in your stack and opt to check. The flop comes 8♥ 7♥ 3♠. You check and the cutoff bets 100.

Question 1: Should you fold, call, or raise to 350?
Answer: You checked on this flop due to having a very wide range, although betting may have some merit, depending on what you think about your opponent’s limping range (which may or may not contain a lot of middle cards.) Because your range is so weak in general, you should usually not bet too often.
Facing the small bet, middle pair is certainly good enough to call. Raising is not a good option because your opponent will likely only continue with mostly better made hands and high equity draws. 

You call the cutoff’s bet, growing the pot to 530. The turn is the 5♦.

Question 2: Should you check, bet 220, or bet 330?
Answer: When the turn is excellent for your range, leading for a tiny amount to push your range advantage becomes a viable option. This allows you to get value from some worse made hands like worse pairs while also getting protection against various overcards.
If your opponent goes all-in over your lead, be prepared to call off with your pair plus junky draw. 

You decide to bet 220 into the pot of 530 and your opponent calls. The river is the 4♥.

Question 3: Should you check, bet 400, or bet 800?
Answer: Even though you improved to two pair, there are a lot of flushes and straights possible. Because of this, betting large or going all-in are not good options. Betting small has some merit if you think your opponent will call with lots of marginal made hands, like one pair. Checking to induce a bluff (which you would call) is also fine. This is a tough spot, but betting small is probably ideal. 

You decide to bet 400 and your opponent goes all-in.

Question 4: Should you call or fold?
Answer: This is a spot where most players are simply not bluffing anywhere near often enough. In order for them to bluff, they need to know that you are capable of making a disciplined fold while getting excellent pot odds, which many players simply cannot do. 
You decide to fold to your opponent’s all-in. They do not show their hand and they win the pot of 2,450. ♠