I noticed in the village most of the "for emeralds" trades were X'd out. Do they grow back over time?
Not over time. Trades are refreshed by trading for the last trade in their menu. Let me see if I can explain:
Part 4: The Mechanics of Trading
Each villager has a job. Farmer, Butcher, Blacksmith, Librarian or Priest. They start with one trade. Make that trade and, since it is the last trade on their list, when you exit the menu the villager will sparkle green, and then have purple swirls surrounding them for a while. I think this happens every time you make the last trade on their list, but it doesn't always mean they've unlocked a new trade. Sometimes all it takes is one trade to open up the next one, sometimes that trade has to be made multiple times.
Each trade has a limit on how many times the villager will trade it. Somewhere between 3 and 13 according to the wiki. Once you reach this random limit, the villager will just grunt and the trade won't go through. If you exit the trade interface and return, that entry will be X-ed out.
Every time you make the final trade on a villager's list, it will open back up old trades. This is why a lot of villagers have X-ed out offers, because it's generally most efficient to make as many of the lower trades as possible before making the final trade on the list, especially if that last trade is buying something otherwise unwanted.
Here's where it gets complicated. According to the wiki, there is no limit to the number of new trades a villager will offer, but they can only have one offer of each kind. So when a new trade is unlocked, it has a chance to overwrite an old trade. So a priest who trades 1 Emerald -> 4 Bottles O' Experience might unlock the new trade of 1 Emerald -> 2 Bottles O' Experience, and the original offer will no longer be available. However... I don't know how accurate this is, or what the rules are. A villager can offer one trade for iron boots, and another trade for diamond boots, but I don't know if they'll offer two different trades involving enchanting books. I don't even know if old trades getting overwritten happens at all, since I haven't been keeping close enough track of villagers to be sure. I do know I can't seem to find the villager who was trading for Respiration 3 books, but maybe I was just having bad luck. It's hard to track these guys down.
The way I trade in short:
1. Look through list of trades, and figure out which ones I
want to make.
2. If any trades earning emerald are not the last trade on the list, make those until they are exhausted.
3. Once all profitable trades are exhausted, then make the final trade on the list, to refresh previous trades and in hopes of unlocking the next level.
Generally I will make all profitable trades, regardless of if there is a better trade somewhere. I generally don't worry about the difference between getting an emerald for 14 coal or for 20 coal. If trades could be made an unlimited number of times, I'd be making a list of the absolute best trades for any item, but since it's hard to predict what trade will be necessary to refresh a villager's offers (and it's a pain to hunt down specific villagers), I just make whatever trades I can.