How popular is Dugin in Russia?
I don't know. He is not among those who contend for power and end up in jail for it. He is more of a thinker. We was connected to Limonov, -- a colorful man, a great poet and a founder of National Bolshevik movement. That earned Limonov some following and even a jail term for armed insurrection, no less. Both are basically proponents of the restoration of the USSR, albeit in some new form, and hate the Western political and economic system.
Dugin is however, a believer (Orthodox but with a twist) and that separated him from Limonov who has no discernible religion.
But these are personalities. The Eurasianism, however, seems to be a conscious Putin's policy: there is a clear course on irritating the US, and rapprochement with everything in Asia that would sit down with them: Iran, China, Assad, domestic Muslims. Russia has its own immigration crisis: residents of the Muslim periphery flood ethnically Russian territory in search of work, mosques are being built at a dizzying pace (alongside Orthodox churches) and Russian cities take on a bit of that Central Asia look. That troubles the general population, which, however, remains mostly docile; it also greatly troubles the few Russian conservatives and nationalists -- who tend to see Russia as a decidedly European power that colonized Caucasus and Central Asia. They do not have a voice other than in the blogosphere. It is hard to say if they influence anyone. Greater influencer seems to be ethnic crime: rape and bar brawls, where Russians, not used to street fighting and not used to carrying knives and guns, come out victims. This causes anger and may result in pogroms against the Asians. All that is sad to watch, and Dugin has got to like it.
He is more popular in the Russian Army and in the security establishment (searching for a cause when Marx is dead) than in the office of Putin. But, Dugin has made the strange idea about Euroasianism https://en.wikipedia.org/wiki/Eurasia_Movement acceptable in Russia.
Russia, or persons representing the state, are profiting on the Iranian sanctions and are laundering money and oil from Iran, thus they do not want a solution of the present situation. I anticipate that Iran want to end their dependence on Russia, but the do not know how to do it.
Note that the Russian economy requires an oil price 120-130 /bbl in order for break even of their budget. The next time that the oil price will be parked for months below, say, 80/bbl there will be a new revolution in Russia as they run out of money. Putin knows this and that is why Russia is supporting problems in Middle East to keep the oil price high.