After primary phase 1 week, you then transfer to the other bucket or carboy for 2 weeks right? Then do you prime the mix in the second bucket then bottle?
But what I dont understand is if you have a primary bucket with air lock, does your secondary need an airlock too? Some kits have one with airlock and one with spigot... Are these used for secondary fermentations?
Yes, you will need an airlock in your secondary fermenter as well. You could use your bottling bucket for secondary fermentation, but most people will buy a 5 gallon, glass carboy to use as a secondary. If you don't have one, just leave your beer in your primary for three weeks and then bottle.
If you are like most homebrewers, doing this will drive you mad because you can't see your beer. This is why folks rack to glass carboys for two weeks after primary fermentation, but you will make great beer even if you don't do this.
Off flavors from yeast and trub will not develop for months . . . and your beer will be gone by then...