It looks to me like the answers to your questions are right there in the site you linked to:
Parents who permit a child to attend a home school that is up to the standard of Section 26-1, as interpreted by Levisen, are free to decide the manner, time and materials which best suit the learning needs of their children. Parents may determine what type of home-schooling curriculum is best for their students, what materials to use, how much homework to assign, how homework is to be assessed, and what records of the student’s accomplishments should be kept. Testing is not required in the state of Illinois for homeschoolers.
So basically, you have wide latitude (it even uses those words in the next paragraph) in determining what meets your child's needs. If your DS needs 1-2 hours, then he can have 1-2 hours.
It seems the state of IL does require homeschoolers to renew their registration with the state each year, but does not require them to provide any documentation that demonstrates what the child has done the year before. Here in LA, they require a small portfolio of the child's work, or standardized assessment test results. I would interpret that as meaning that nobody will be looking over your shoulder in IL unless there's a reason to investigate. For example, a pediatrician might call in a complaint to the child welfare department if a 9yo couldn't read simple instructions.
It would be prudent to keep a portfolio of your children's recent work on hand, just in case anyone ever asked. And there are places where you can get standardized testing... our DD8 just did two of them. Nobody is going to argue with test results... we just used a homeschool year and assessment testing to grade-skip our DD into the same public school district that adamantly refused to entertain the idea for the last three years.
Also, we frequently refer to our state DoE's "Grade Level Expectations" as a reference for the minimum requirements our DD should be working on, to make sure we're not missing anything. DD is, of course, free to explore as far beyond the minimums as she likes. It looks like IL calls them "Performance Descriptors", and describes them in unnecessarily confusing terms... I feel for you. The "Classroom Assessments" look a lot more user-friendly, though.
http://www.isbe.state.il.us/ils/html/descriptors.htm
