Is there a 'cool down' for villager breeding?
Villagers have reputation as well as willingness. -30 is the minimum while 30 is the maximum reputation. They will stop breeding when you lose reputation.
Here is some info on reputation.
http://minecraft.wikia.com/wiki/Reputation
I have also read 5 or 3 minute cool down after a pair breed for those two that did breed. Untested though!
If two villagers successfully have a child, there is a cooldown period of 5 minutes. However, if breeding is unsuccessful due to overpopulation (or unable to access beds if there are enough), there is no cooldown. They will try to breed again and most likely fail again. Also, when they try to breed (indicated by red hearts), they will consume food levels regardless of whether breeding is successful.
Note that this does not suggest that the food levels will drop to 0 in 1 game tick because the breeding animation takes time to play and villagers only breed during a specific time of Minecraft day.
The above was tested in Minecraft Java 1.16 released version.
Yes. Villagers must be "willing" in order to breed, and stop being willing after breeding.
Villagers can be made willing again by trading with them or by picking up food. I assume you have put the villagers close to or on a farm, and so they will farm and collect food automatically, but it takes a short time for a villager to collect enough food to become willing.
The Minecraft Wiki explains willingness in more detail: http://minecraft.gamepedia.com/Villager#Willingness
Don't forget that the chunks must be loaded for the villagers to breed, and make sure that the requirements listed in the "Breeding" section of the link are satisfied all the time.
Villagers try to maintain their population below 35% of villager house, If you want to get more villager add more doors but make sure it has an "inside" and "outside" space i currently have 15 doors and when im not satisfied with the Type of villager i got, i use sand to suffocate it without losing popularity, By The Way villagers will only go to the houses if its in 32 blocks in a village center