Villagers are all randomly assigned a profession on spawning, and unfortunately, this is an even 1/6 chance for each one. For specifically Farmers (so you can trade) this is then further broken down to the 4 different brown coat professions, ultimately making the chance of a Farmer spawning only 4.17%. Source.
Fortunately, it would appear that baby villagers are also assigned their professions at random, so it is entirely possible to create a Villager Breeder in order to find the Villager you are after, or simply boost the amount of doors you have in your village. Even by simply creating a 3 wide covered platform with in the village, and fill that with doors will greatly increase your villager breeding rate.
Yes. There is a "Claustrophobic" aspect that derives from how the passive mob ai move in minecraft.
Every game tick, passive mobs choose a block within a diameter of 16 blocks to move to.(when you hold wheat, your location is used instead.) If there is not block there, or there is no air above it, they abandon that path, and do not move. This happens most of the time.
If the block they chose is valid however, they will try to move there. If their pathing algorithm cannot find a way to get there, it will keep trying to find one every game tick until it finally gives up and chooses another block, how long it takes to give up depends on game version and type of mob.
What this means is that when a mob is in a pen, if they choose to move inside the pen they just move. If they choose to move outside the pen, (about half the time if they are near the wall, or more if the pen is small) they wait for you to make an opening, then walk towards it. Depending on the proportion of inside to outside this can be more then half the animals at one time.
I have exploited this behavior to create an automated slaughterhouse with pistons, tripwires and fire that turns cows into meals automatically.
If you just want a way to stop them from escaping, you can use trapdoors as doors to your pen, as regardless of whether the trapdoors are up or down mobs see them as a solid block.
Best Answer
This is a bug that still exists in the game. Clearly, I suppose. Point is, your version of Minecraft has nothing to do with it.
I have seen this problem many times, and it seems to be related to fences and reloading the world after it has been unloaded. One solution to your chicken escapee problem could be to dig a two-deep pit for your animals to live in.
...but there's a problem. When you replace the fences your animals have glitched into with solid blocks, you have some slight suffocation problems (same bug). So that's no good without some slight adjustments.
I tried an old method using water, however, animals are somehow more broken now, and sit at the bottom of the water streams and drown.
So I tried another approach: I used slabs for the bottom layer of wall instead of dirt blocks. They'll still keep your animals inside, even if you relog, and with minimal casualties (occasionally, I'd get a few baby pigs suffocate when I relogged, but nowhere near as consistently as without using slabs.
However, I have found some weird behavior using slabs. You can use any other transparent block, but, since apparently baby pigs are less than a half block tall now, you cannot use slabs. Also, if you wish to contain cows, you will need 2 layers of transparent blocks. I used glowstone in this case.
SCIENCE!