What is the limit for calling raises with pocket pairs preflop with this stack size? If everyone folds to the raise except for us, what is the most we can call without it being a -EV play? Should we be willing to tighten up the limit if we will be playing OOP?

Many suggest that you should be getting at least 11:1 on your call against the average opponent. In fact, in his new book Ed Miller suggests putting in no more than 8% of the smaller stack preflop.

With 50bb you can't call raises to set mine. For it be +EV you need to be getting something over 10-1. Heads up against a villain competent enough that he won't stack of with a single pair most of the time, I would want something like to 20-1.

With 50bb you can barely afford to limp in with pocket pairs. You can't afford to limp in and then fold flop very often before you stack withers away. So even there you can't play all of your pocket pairs, just some when the situation is good. From LP or SB in a situation where you don't expect a raise after you, it would be OK, but even there you would want the pot to be multiway already to give you better odds.

being oop does make it a factor and you should be giving yourself closer to 13-15 to 1 on a call. But it depends on the dynamics. if the opponents are very lagy you can afford 11 to 1 since you can expect all the money to go in. if your opponents are more competant, its goint to be harder to build a huge pot oop and get stacks in

You guys are way too tight and wouldn't be able to survive in a lot of CA games where BI is between 20-60bb.

Set mining without antes 20-60bb is absurd.

You should be raise/jamming these hands and or getting it in a decent amount when you don't make a set. This isn't set mining.

As for set mining with 50bb, first of all if you're a set mining nitbox then you don't want to play 50bb. You can set mine more effectively in multi-way pots where your implied odds are better. 11:1 posted above seems like a decent guideline - so if it will cost 5bb to play, you will need to scoop a 60bb pot to get involved.

In MW pots this is achieved much easier than hu. HU set mining vs a 3x open vs a non drooling idiot donkey and or nitbox with a big pair a huge % is probably not going to work out so hot.

Position also matters including position relative to the original raiser.