If these gold coins are minted by that country's mint than yes, they are legal tender in that country at their face-value. But this is still a foreign currency in other jurisdictions, so I doubt it strongly that you could officially pay taxes directly with them anywhere in the world except a country of origin...
Only for the face value portion of the exchange. The commodity value is taxable separately.
That was exactly my point. Is it really possible to pay taxes
directly (i.e. bypassing banks and that kind of things) with gold and silver coins in the USA at their market price?
No. If you don't pay the commodity portion of the tax due, you will go to prison and/or pay hefty fines. There are cases already.