Just concentrate on Tadkerson's first post in this thread. That gives the basics. I agree some of the other posts can be confusing.
There are two basic ways to make chicks that can be color sexed. With red sex links, you get chicks where the males have yellow down and the females have reddish down. The actual shades can vary, but this is the basic principle.
With black sex links you get chicks that have a white spot on their heads if they are male and no white spot if they are female. They don't even have to be black. They just have to be a color where you can tell if they have a white spot on their head or not. Again, there can be a lot of variation and whether you can even see the spot, but the basic principle is spot or no spot.
What you get with your Ameraucana depends on a couple of things. One, is he a true Ameraucana or an EE (Easter Egger)? There are a whole lot of threads on this forum about that. Ameraucana is a very specific breed where the EE is just a mix that can lay a blue or green egg. If you got your Ameraucana from a hatchery, he is an EE, not an Ameraucana. Anyway, that is a whole other topic and thread. The other thing is what is his genetic makeup? Is he barred or does he have the two gold genes? Regardless, you will not get a sex link with a Rhode Island Red hen, nor an Australorp. If he is not barred, you will get a black sex link with the Barred Rock (BR) hen. Depending in what colors and patterns he contributes, you will probably be able to see if the spot if it is there, if she is a true Barred rock hen and is not a cross herself. One potential problem. If you hatch eggs from this rooster and the BR hen and Black Australorp (BA) you will not know which are the sex links. If he is not barred, the chicks with the white spot will be black sex link males, but the black chicks without a spot may be black sex link females or either male or females from the Australorp.
Does a sex link hen produce more eggs than a non-sex link hen? It makes absolutely no difference if they are a sex links or not. If the parent stock are good egg layers, the offspring will almost certainly be good egg layers. If the parent stock are not good egg layers, the offspring probably won't be either. This is not tied to them being sex links.
Where it gets set in many people's mind that sex links are automatically good egg layers is that the benefit of producing sex links is that you know you are getting either a male or female. Since many people want females that are good egg layers, the hatcheries practically always use parent stock that are good egg layers, so the sex links you get from the hatcheries are almost certainly going to be good egg layers. If you cross say a RIR rooster with a BR hen that come from good egg laying stock, you will get a black sex link that should be a good egg layer. But if you cross a BR rooster with a RIR hen from the same stock, you will not get a sex link but the offspring should still lay just as well. If the parent stock of either mix are not good egg layers, the offspring probably won't be either.
I have no idea what a high breed hen is. The earliest I have ever had or heard of a pullet laying is 16 weeks. While that is not totally unusual, it is not that common. Three months translates to 13 to 14 weeks. That sounds like a sales line to me.
Editted to add. High Breed probably means hybrid. Nothing really special about that.
