Overpair vs Possible Set Game Theory Question

[ZeeJustin]

Situation 1:
$5/$10 NL

Player in EP limps. EP has a pair other than aces. Each pair is equally likely. It folds to MP who makes it $44 with AA (face up). Only EP calls.

Flop: Q72 rainbow - $100 in pot ($3 rake was taken out)

EP checks. MP bets $100.

Action is on EP. EP has 2 options, all-in or fold (both players started hand w/ $1,000 stacks). After that, MP obviously has 2 options, call or fold.

Observations:
EP must bluff here for optimal strategy. The question is how often?
To make the math easier let's assume when EP has a set, he's a 10-1 favorite. When he misses, he's a 10-1 dog.

Questions:
1) What % of the time should EP move all-in to give MP a break even strategy? I.e call and fold have equal equity.
2) is this optimal strategy for EP? If not, what is, and then what is MP's optimal strategy?

Situation 2:
Same situation as before, but now EP has 2 different options. He can either fold, or raise to $300. After that, MP has 2 options, fold or all-in. And finally, EP can call or fold.

What would be the optimal strategy for each player in situation 2?