Good subject (in all meanings of the word...) !!! :thumbsup
Of course, as already said, red and black caviar are not the same, and of the same quality, even if I like both.
The red one is not expensive in Russia, and you can find it easily. It is moreover for sale in ALL duty free shops ar Rusian airports. No pb for exporting it, and importing it when you arrive in your country (at least in France). Moreover, airport duty free shops are (according to me) the best place to buy it, as the cold chain is kept at maximum, even if you can find lower prices downtown.
The black one is another story, with its three qualities : Beluga, Sevruga and Oscietre. You can find it everywhere in the world in fine comestibles shops. I have good addresses here in Paris... but it is extremely expensive. Nearly the same prices in Moscow's dedicated shops. Th best quality and price I have bought in Russia are on the occasion of trips in the Far Eastern area (Khabarovsk, Komsomolsk-na-Amure).
The black caviar is not for sale in airport duty free shops in Russia... but is in Kazakhstan...

But, I have never seen there a very good quality.
It is extremely difficult to find it today in Iran, as the Caspian sea is more and more polluted.
About export, I think the international conventions for protecting the strurgeon species limit to an export of 200g / person (tbc).
About stories : I have two.
I have eaten, last December, with some friends, black caviar with a good bottle of Khabarovska Vodka (ice filtered), in the middle of the Amur river, totally frozen (both the river and us), by -36°C (-33°F). Around, us, nothing and no one, except fishermen digging holes throught the ice... :thumbsup
A second one, older : in 1991, in Dubai, at a gala dinner in the palace of one of the Al Maktoum princes, I have litteraly be served black caviar with a ladle...
Cheers.
Ch.