"Cycle- what cycle year will STAA be following next year. This year all of my boys have followed American History, we will cycle back to Ancients with our co-op (Catholic Schoolhouse) and hope to do that with our curriculum at home."    

Our cycles run Greek, Roman, Old World, then New World.  Then they repeat.  We like to sneak a year of Ancient history in for Grade 2, 3 or 4 for the young family when possible and then start the Greek, Roman, Old World, New World cycling after that.  At the grade levels you refer to, doing a Greek year wouldn't be a problem (but we will move your Gr. 9 students to the New World/US cycle, note).   I don't believe our history cycles coincide with Catholic Schoolhouse.  History is a per-family endeavor, not a school-wide endeavor.

"History- I see that each grade level is designated a history focus (online under the grammar tab of the website). I will have an 8th, 7th, 5th, 4th, and K student and would like to group teach them as many lessons as possible. I typically try to do this with History, Science, and Religion."

We tinker with our Religion/History/Literature/Science/Fine Arts units (they resemble a unit study format) per family, except in our high school diploma program where the years build on themselves in study skills and study methods.  Our high school diploma program is more structured to accomplish the Catholic classical liberal arts college prep model.

"Literature - Because I have a few boys who really struggle with Language Arts, I would like to better understand the Literature portion of the STAA curriculum. [The advisor] mentioned a Great Book's preparation. Is there any information you can provide that will help me understand this component of the program?"    

Language arts and literature are separate courses in our program.  Language Arts develops and crafts reading, spelling, formal composition, formal grammar, punctuation, and cursive.  Literature trains the students in literary analysis, critical thinking, moral reasoning, note-taking, notation, logic.  Mortimer Adler has several books out about Great Books.  There are myriad articles online regarding Great Books life-time pursuit.