1. How do I use those AR codes?

You need an Action Replay cheat device.

Couple of minutes. Then just walk around till the Egg hatch

1. You need to input the codes on the correct screen.
2. It depends, if they like each other a lot, then an egg will come faster. If they dislike each other more, then it will take a long time, or never.

1) You need an Action Replay device first to put the codes in, then you just select them to use them, and they usually have some preloaded, too. It's around $25-$30 to get one. It's a cheating device and can mess up your game-so be warned not to use too many codes at once and try to avoid walk through walss codes, and don't fill up your inventory with a lot of "infinite" items-like unlimited all balls codes-because you'll never get rid of it and it'll eventually make it so you can't store your stuff. Never use all key items either! No need to, and you can't get rid of those either!
2)Well, it depends on the Pokemon you bred. If you use ones with 2 different ID numbers (like ones you got from another game or someone else), it will tend to be quicker to get and hatch an egg. If you're waiting, just ride your bike around, then go back by the daycare and see if the guy's outside waiting to talk to you. Also, how much they like each other will help them breed quicker, too. Usually it's pretty quick-hatching usually takes longer, but if you have a Pokemon with Magma Armor ability in the first spot when you have the egg in your party it'll make it hatch faster.