I am filing Illinois state tax return. For the education expense in the section "Illinois Credits and Taxes", are SAT test fees and college application fees regarded as qualified education expense that can be entered here? Thanks.

Sorry, no.  Here are the expenses that qualify:

What are qualified education expenses?
In general, qualified education expenses are the amounts paid in excess of $250 for tuition, book fees, and lab fees at the school where the student is enrolled in kindergarten through twelfth grade during the regular school year. Specifically, qualified education expenses include the amount of tuition (including summer school classes required for elementary or secondary graduation requirements), book fees paid for the rental of books that were required as a part of the school’s education program. lab fees paid for the use of supplies, equipment, materials, or instruments that were required as part of a lab course in the school’s education program.

https://www2.illinois.gov/rev/research/publications/pubs/Documents/pub-132.pdf