Trace the device that made online purchase
Few years back, I had bought an Ipad and I had set my apple_id along with my credit card information in this Ipad. Few months before I gave this Ipad to a friend and the serious mistake I made was I did not delete my apple_id and credit card information. The following month I was very surprised to see in-app purchases made through my credit card. I checked my email and found that someone found the bill summary of online purchases made mostly throught online games such as candycrush, racing games, etc. I thought my friend made these purchases and confronted her but she said that she never made these purchases. And in the bill summary I can only see the apple_id, app name, company name and the purchase amount. I want to know if I can somehow know the device personal information that made these online purchase (such as device serial number, imie no, iccid, etc) so that I can confirm if the purchases were made from that very ipad or someone else has hacked by apple id.
You can't find out what device made the purchase, that isn't stored anywhere that you have access to.
If you haven't already done so then you should change your account's password e.g. by logging into it via the Store > View Account menu option on your computer's iTunes, logging in via the 'manage your apple id' button on http://appleid.apple.com, or tapping on your id in Settings > iTunes & App Store on an iOS device.
When you gave the iPad to your friend did you log out of your account on it and remove all of your content from it ? Any apps that you left installed on the iPad will have remained tied to your account, so only your account would have been able to do in-app purchases in them - unless your friend delated the apps and downloaded them on their own account.
If you didn't make the purchases then contact iTunes Support : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption