I booked flight and got booking details with TOTAL paid in USD, no break-down. Few days later, I called help center (they do answer very quickly and are very polite). Lady sent me receipt with break-down in EUR.
When I asked how much I should have paid in dollars - she named amount which is 40 less than what I paid so I had to open contact us request for USD invoice.

Is that a standard practice ? I do not see anything on the website warning me as consumer that buying in currency other than EURO will result in extra charges.
Had I gotten a detailed receipt in USD right when I booked - I would have had a chance to cancel and rebook (I think) under 24hr policy.

Yes, I charge in local currency when abroad. Never crossed my mind that major airline direct website will be playing conversion game without any type of consumer warning or proper choice.

I can't say if everyone over-charges for transactions in foreign currency as much as Aegean does (which is a lot!), but pretty much everyone over-charges more or less in such cases (one easy example is Amazon, even if it's by something like 2% more or so).

Basically all you needed to do was to try and switch currency on Aegean's website (to Euro), then use a currency exchange rates source (xe comes to mind) and the difference would have been immediately clear. Since this is common practice among businesses of all kinds it's very unfortunate you didn't realize it before making the booking.

I don't think getting a receipt in usd would have helped much either, I think the 24h rule is a strictly US thing (unfortunately for everyone else too) and I don't believe that simply visiting Aegean's website and paying in dollars qualifies as a tickets sale within the actual country.

I also doubt there would have been any clear indication of a "currency exchange fee" or something like that in the receipt, they would have simply written down the prices in usd ss they would have in eur, only they would be something like 10% than what the actual exchange rate would dictate (plus braking down the total amount into smaller ones in the detailed receipt would actually make it more difficult to spot the difference in the exchange rate).

Yes, unfortunately, all Aegean flights on the website are priced and sold in EUR, and they apply around 5% DCC mark up for all other currencies. I haven't found any other airline which does this without a proper warning, so it is a deceptive practice. See this thread:

Aegean gets on board with dynamic currency change?

Usually major airlines only allow you to book online in the currency of the first departing country (or a stable currency that the first departing country uses). A few airlines allow choice of currency but they tend to use the IATA exchange rate. I suppose if one was thinking really carefully, one would notice that A3 doesn't fly to any USD country so shouldn't need to offer USD payment, and it also offers payment in AUD, BRL, CAD without flying to those countries which might possibly raise suspicions.

Based on your conversation with the agent, it seems that if you book on the phone A3 may also be able to use the IATA exchange rate, but that incurs a phone fee; or maybe the agent just typed the euro amount into google or xe.com...

I book in EUR on the website and use my no foreign exchange fee credit card to purchase the tickets. Never select a non Euro currency.