Is Customs, on departure, before or after the security checkpoint?
There's no customs leaving a country. Now, what's the 'vat stamp' business about? Do you mean vat refund? Are you asking about duty free? What's up, exactly?
Yes, it is still called Customs, regardless. Rick Steve's even calls it Customs. I want to know, if you will read my post, is the office to get the VAT stamp, at Fiumicino, before or after the security checkpoint? I've been through there before, but don't recall. http://www.ricksteves.com/plan/tips/vat.htm
VAT stamp for VAT refund.
For a VAT Refund, you'll look for Dogana (Customs) or a directional sign that says " VAT Refund." As far as where they are located at FCO, it depends on which terminal you are departing from. If you're leaving on a US flagged airline from Terminal 5, hen you will get your VAT refund there in Terminal 5 - before heading out to the buses and the gate areas. If you are leaving from FCO to a NON-Schengen country other than the US (or Israel on El Al), you'll probably depart from T3. There is a Dogana (Customs) office before security (on the back wall) and ALSO ONE ON THE OTHER SIDE of security ... used to be just after passport control. There is no VAT Refund office departing out of T1 or T2 as these airlines primarily fly to Schengen area airports. But if you have arranged separate tickets (or some other unique routing), you can enter the secured area at T1 and staying behind security, walk over to the "VAT Refund" desk behind T3 security. Back when this was "Terminal C" (prior to October 2009), I often got my refunds here behind security. They seemed to ask fewer questions, did not care to see the merchandise - but that was back then; So you do have a few options when getting a VAT refund. Head to the Maps page at FCO airport website for more specific directions. Good Luck!
If I am reading the T5 map correctly, acquiring the customs stamp comes before security and passport control.
Unless they've moved it, you're correct. After you check-in and get your boarding passes, you can go to the VAT Refund areas in either T3 or T5 - before you do security. Again, T3 also has a counter AFTER security.