Actually, Easter Eggers bear almost zero relation to Araucanas. The only real similarity is that some Easter Eggers can lay blue eggs (though more often they lay green or sometimes brown eggs). The main reason people get them confused so frequently is that hatcheries tend to label their Easter Eggers as "Araucanas" or "Ameraucanas," using the name of standardized breeds to market their non-standardized production-type colored egg layers.
To answer your questions:
1) EE roosters can be mean or they can be docile. EE's are a genetically mixed bag so you can never predict what you will get. "Purebred" Araucanas are usually very docile.
2) Araucanas are very broody. With EE's, some hens may be good broodies, others may show no interest whatsoever. Again, there's no telling what you might get.
3) An EE is most often a mix crossed with a mix crossed with a mix for many, many generations. Usually they received the traits for colored eggs and beards/muffs from Ameraucana breeding stock (a different blue-egg-laying breed) somewhere in the recent or distant past.
4) SIMILARITIES: Some EE's might lay blue eggs. Many EE's have pea combs. Occasionally you might see a rumpless or tufted EE X Araucana mix.
DIFFERENCES: Araucanas are a breed listed by the Standard of Perfection; EE's are not. Araucanas are rumpless; EE's are tailed. Araucanas have pea combs; EE's may or may not have pea combs. Araucanas are supposed to lay blue eggs; EE's most often lay green eggs, and sometimes brown. Araucanas have tufts; EE's do not. Araucanas do not have muffs or beards; EE's often (though not always) do. Araucanas come in standardized color varieties; EE's do not. Araucanas must have the appropriate leg & skin color for their variety; EE's have all sorts of leg colors. Araucanas can be shown; EE's will usually be disqualified (though sometimes in 4H and Youth events judges will make exceptions). Araucanas are usually extremely docile in temperment; EE's are unpredictable and vary from bird to bird. Araucanas are small birds; EE's are medium or large. Araucanas are fair layers; EE's are great layers. In other words, they are not alike at all!
Here are a couple pictures, I chose these pics because the birds' colors are similar but their physical differences are obvious:
Araucana:
Easter Egger:
Those were good questions. If you'd like to take a look, I have a page on my website where I briefly explain the differences (with pictures) between Araucanas, Ameraucanas, and EE's:
http://www.araucanasonline.com/page5.html
I hope this info has been helpful!