I want to know when I purchased and activated my Apple 32 GB iPhone.

Look at the date on the receipt.

If you're trying to find out if it's still in warranty, you can check here:https://checkcoverage.apple.com

Your receipt has this information. Also, you warranty starts on a day of purchase.

You can also try to use https://www.imei.info

You can find your IMEI in the phone settings

No 3rd party has legitimate access to that information.