Is there a way to find out information on battery through macbook serial number?
Unfortunately, information would not be attainable simply through the serial number. It is unlikely that you obtained the incorrect battery, since AASP's source their parts from Apple to perform warranty-service repairs. I poked around online and noted that you are not the only one who has the bq20z45 part number from SMP, nor the only one to have a Full Charge Capacity different than ~8000. I found this via various user screenshots on Amazon. 

Likely, the battery is correct for your unit and will function as expected. If not, all warranty repair services are either covered by your Applecare Protection Plan or, if out of warranty, 90 days from date of service. Should you continue to have concerns, I'd call the AASP back to verify that you got the right item.

EDIT: It may be worth it for you to calibrate your battery. Charge all the way to 100%, then unplug the unit and use it until it dies w/o charging it up again. Repeat once and that should get your battery reporting accurately as well.