Minecraft – How long does it take for villagers to breed

Most of what you're asking can be found on a couple of articles on the minecraft wiki site, but I'll summarize the big points:

• Villages are specified by the existence of doors that meet certain conditions. For a door to be counted as "in a village," the door must have more blocks on the outside than on the inside and a villager must exist nearby - no more than 16 blocks horizontally and 3 to 4 blocks vertically. A block is counted as inside if it is shaded from above. A block is counted as outside if the sun hits it from above. Here are some common techniques for registering doors.

• If the distance requirement for a villager nearby a door is not met, the door can become unregistered after some time. That can be resolved by destroying it and replacing it.

• Each door can support .35 of a villager, i.e. you need about 3 valid doors for each villager (more precisely, every 20 doors support 7 villagers).

• The boundary condition seems a bit hazy, but the 16 block requirement in the first point seems to imply that it's 16 blocks from the most outlying door. However, villagers can move up to 40 blocks beyond that before they actually unregister from their village.

• You must have at least two villagers if you want to start an entirely new village. That means you've either got to find a village and transplant villagers from there, or cure Zombie Villagers using a Splash potion of Weakness, Golden Apples and time.

  • Once you have two villagers, you can have them create new villagers by "making love" (villagers are genderless, so any 2 will do).

  • Villagers will attempt to birth new ones when the village can support more than the current number, as per the third point (doors can support .35 of a villager).

• Iron golems spawn when there are at least 16 adult villagers and at least 21 valid doors.

• Iron golems and villagers both will wander aimlessly if they are not created naturally or are not in a village, respectively.

This information is valid as of snapshot 12w21a, version 1.3.1.

EDIT: To answer the more specific questions OP had...

I don't think anyone really knows, except for the developers, where the hard cutoff for the village is, or if this is one. Apparently at some point, Notch was going to put in some physical boundaries for the villages, but they might not even exist in newer releases.

This mod claims you average out all the locations of the valid doors for the village center, then that the boundary is the largest distance from the center to the farthest house (or 32, if there are no other houses) but it's not clear whether the mod maker thought of these arbitrary boundaries or whether they're actually in the game. I'm going to stick with what the wiki implies and say that villagers register to a village and probably wander up to 16 blocks beyond the outermost doors, and only deregister from the village if they're beyond 40 blocks.

This applies to Minecraft versions 1.8.0 - 1.13.x

The 1.14 Village and Pillage update changed breeding mechanics again

That your Villagers are entering into "mating mode" (i.e. they occasionally have hearts floating out from their bodies) is a good sign. It implies that the Villager's surroundings are suitable for breeding to occur.

However, with the 1.8 release Villager breeding has been tweaked. Villagers now also have to be "willing" to breed, being in "mating mode" isn't enough anymore.

From the Minecraft Wiki:

Willingness

Additionally, villagers must be "willing" in order to breed. After mating, they will no longer be willing.

Villagers can become willing by the player trading with them. Willingness is granted the first time a new offer is traded, or at a one-in-five chance on subsequent trades. This will not cause them to immediately seek out a mate, however.

Villagers can also become willing by having either 3 bread, 12 carrots or 12 potatoes in one stack in their inventory. Any villager with an excess of food (usually farmers) will throw food at other villagers, allowing them to pick it up and obtain enough food to become willing. You can also throw bread, carrots, or potatoes at the villagers yourself to encourage breeding.

That would suggest that it's this new "willingness" mechanic that's actually holding your village back. As the article suggests, you should be able to make the Villagers more "willing" by throwing enough food at them. A caveat though: don't expect this to be quick when your initial population is small!