I see some advertisements about trading Amazon gift cards for BTC but how does one does that?
Depends what the ad is/was for. This is a 3rd party deal. Amazon is currently not accepting BTC.
I have an Amazon Gift Card $50 + and I would like to sell it here for BTC and I would use an escrow service but how does the trade happens?
You open a thread in the digital good section and see what offers come in. State that you want to use escrow.
Who sends who first?
The buyer (B) will send the BTC + fees (usually buyer pays them) to the person doing escrow (E).
You await confirmation from E and give code to B.
E awaits confirmation from B that the code is in order.
E now sends BTC to you.
And how is it confirmed?
The buyer will have to confirm this via Amazon.
What if the buyer gets the Amazon GC, uses it and claims that he did not received any money in his Amazon account. In which case the escrower would transfer his BTC back to him?
To avoid this E can redeem the card and make a new one for the same amount. This will cost no fee from amazon.
Is there way to confirm the authenticity of Amazon gift cards prior to purchasing them?
I am not 100% sure but you probably can cancel the redemption. If not you can just generate a new code.