No, you don't have to file F3520. Per the form's instructions, you should file F3520 if you received:
Thank you for the clarification and you are right... I was simply focusing on the form itself... As a receiver of a gift form covered expatriate, you don't have to report if you received $15,000 or less. You would have to pay tax on the gift in excess of the $15,000. That would not be on F3520, you would file an Estate tax return. More details here, if you'd like.
You are correct- annual exclusion ($15,000) does apply in your case.
As to the gift - it is on annual basis... you can give $15K to a person during the year... it can be done in increments, as long they don't exceed the annual amount. Theoretically, if you send 20K to a friend and that friend does send back $15K, then yes - you only gave $5k. But practically, be sure to annotate each transfer so that you can easily prove to the IRS ( if needed) which transaction is gift and which isn't.