The blue in an Ameraucana is the Blue/Black/Splash (B/B/S) type of blue. It should be pure for extended black and it is split for the blue gene. That means it has one blue gene and one not-blue gene. It can give either the blue or the not-blue to its offspring, but they will all get an extended black.
The way the blue gene works with extended black is that two not-blue genes gives you a black bird, one blue gene and one not-blue gene gives you a blue bird, and two blue genes gives you a splash bird. If your Ameraucana rooster is a true Ameraucana, it will give an extended black gene to all of its offspring and may or may not give a blue gene to its offspring.
I'm not sure what "blue" the Andalusian or Maran have. I think the Maran is the same Blue/Black/Splash genes as the Ameraucana, but I think the Andalusian has a different genetic make-up to get blue. But I'm not 100% sure about either one. If it is the same B/B/S genes, you will get some black, some blue, and some splash from this cross. You should also get blue, black, and splash if you breed two B/B/S Ameraucanas.
Buff is a bit tricky. There are different ways to make buff and it can have some interesting effects. In theory, crossing a B/B/S blue Ameraucana with a Buff Orpington will give you blue and black offspring, but I would not be surprised to see a lot of buff on it too. I've seen pictures of really pretty chickens with a cross between a buff and black.
Your Speckled Sussex hen should give you both black and blue chicks. You could easily get a few red or gold feathers scattered in there, especially with the male offspring, but these should be pretty basic black or blue.
Your B/B/S rooster over a Barred Rock hen will give you sex links. The males will be barred and the females will not be barred. Some chicks will be black and some will be blue. You should be able to see the spot real well on the black chicks but I'm not sure you will be able to on the blue chicks. I think you will be able to but I haven't had any blue chicks so I'm not sure what the down actually looks like.
The way the egg color genetics work, the Ameraucana should be pure for the blue gene and it should have no brown. There is one pair of genes that determine the base egg color, either blue or white. Blue is dominant, so if the bird has just one blue gene, the base color will be blue. But there are a lot of different genes that determine brown. How these different brown genes go together determines what shade of brown gets put on the egg. This might help explain how it works.
Base blue + no brown = blue
Base blue + brown = green
Base white + no brown = white
Base white + brown = brown
Chickens inherit these genes from both parents. If your Maran lays dark brown eggs, you should get olive green eggs from that cross.
Since the blue egg gene is dominant and a true Ameraucana is pure for the blue egg gene and has no brown, all his offspring will have one blue egg gene. So they will all be either blue or green, depending on what the hen contributes in the way of brown.
I don’t know if the beard or muffs are dominant or not. I can’t help you with that.