Yes, you will see an approval within the next few days (and I am sure its already showing approved online). The EAD is seperate and in my expereince will lag the AP by 2-3 weeks. Yes the fingerprinting LUDs are reported right away, and some folks even get another one the day after (maybe thats the results of the FP)
I got second LUD next day. Wish that may be for name clearance.