I just called USCIS (800-375-5283). Here are the answers to those items:
A# -- Your EAD A#. (I graduated 7 years ago).
Class of Admission -- Your visa class used for your most recent entry to US. I enter US with F-1 visa many many years ago, and never left since then. So I should put F-1.
Current USCIS status -- I have H-1B now and my I-140 was approved. So fill H-1B.
Hope the above useful for other applicants.