I think most of the rest of your questions are closely interrelated, so we don't actually need to answer them all separately:
- Can a character hide behind a barrier, then pop-up to attack in the same turn?
- Essentially spending a short movement and firing in the midst of that movement?
- This would take two actions, yes?
- The character doing this would be Blocked until they popped up?
- Are there any "snap shot" penalties for this quick action?
Kind of. You can shoot, and then move to block Line of Sight. Or you could move to gain LOS (after previously being blocked from view), and then shoot. But you can't shoot in the middle of a movement, each action needs to be completed before you start the next. So you can't gain LOS, shoot and break LOS again in the same turn unless you have three actions (and most characters have only 2 unless they spend their precious Luck dice).
I think most of the "popping up" activities you're talking about are below the level of detail of the simulation in WOIN. That is, your character may be doing them, but they should just be part of the narration of the results of rolls, not actions with discrete mechanical effects. For instance, if somebody shoots at you with a -2d6 cover modifier and misses, you could describe that as your character ducking to avoid the shot before popping back up. It's similar in your question about snap shots. If you run around a corner to gain line of sight on a hidden enemy and fire at them and miss, you might blame the poor effect of your shot on the hastiness of your actions. But mechanically the only real thing going on here is that because you moved, you didn't have an action to Aim before shooting (so you passed up on a +1d6 you could have had in another situation where the enemy wasn't initially blocked from your view).
Cover is very strong in WOIN, especially when your die pool is small, as it will usually be early in a campaign. A big tactical choice players have to make each round is between aiming and shooting, shooting twice, or moving to a new position (and the next good position will often be two or more move actions away). None of the options is always better than the others, and you often want to mix them up, e.g. staying in cover for a few turns and double shooting, aiming and shooting when you don't have a clear shot on somebody out of cover, and then moving to a new position when an opportunity for a Crossfire comes up, or after you've been pinned down by incoming fire for a few rounds.
- Without Cover, the above character would be vulnerable to Overwatch, yes?
I understand the combat rules are designed to keep things dynamic, encouraging movement (which they do!). But it seems common to me in movies where a group takes a position (say in a ruined building) and defends it, using the walls for cover -- like in a Western where they stand behind the wall at the
same window, popping out to shoot. For WOIN combat, it would make better sense if the defenders keep moving 10' each turn, taking up different positions, to keep the attackers from gaining large Overwatch bonuses -- switching up which openings they fire from.
- If three defenders are switching around which openings they fire from, but are firing from the same three openings (just moving or trading positions), does the Overwatch bonus apply to the position? Or is this good enough to reset the Overwatch bonus each turn?
I think you were mixing up Overwatch and Pinned Down in your last few questions, as they don't really make sense as written. Overwatch is an action you can take on your turn that lets you shoot at anyone you who moves into the open where you can see before your next turn (up to a limit based on your INTUITION, though realistically your attack die pool will get pretty small after the first two or three shots, since there's a cumulative -1d6 for each shot after the first, so you may not even bother with the rest). Pinned down is a bonus to hit a target that hasn't moved for several turns. They rarely mix together.
Assuming you were asking about Pinned Down, I think it would eventually apply to a bunch of cowboys sharing a few windows as their cover, because you don't reset the pinned down modifier if you move back to a location where you were pinned down before (though maybe the AGI vs INT test to hide can reset it even in that situation). If the cowboys stay in a besieged building too long, they're eventually going to get unlucky and catch a bullet. Going for a strategy where they shoot twice each turn without moving might even be better than one where they spend a lot of actions changing windows, as with heavy firepower they may be able to kill or drive off their enemies before the modifier for being pinned down gets too high. Shootouts usually don't last too long!