Armenians I assume would back Asad since the Armenians have warm ties with Iran, and mistrust anything that Turkey is involved with. Assyrians/chaldeans on the other hand are joining the Kurds under the KRGs influence (through pro-Kurdish Assyrians in Iraqi Kurdistan).
Iraqs Maliki is really nervous with the whole situation.
I find it strange that you don't know about it to be honest, just to show how the media is silent when it comes to Kurds. Yes, they are oppressed, Kurdish is banned, the names are banned, there are 100,000's of Kurds without citizenship and basically Kurds are third class citizens. Kurds also had an uprising in 2004 which was brutally put down by the Syrian army.
Honestly have no idea. Pretty strange that Kurds get screwed wherever they are; Iraq, Syria, Turkey, etc...
Syria is generally quite tolerant of Christian, Druze, etc... minorities; because a minority itself (Alawites) has a lot of the power in the country. So no idea why they would be intolerant towards Kurds.
I know there are quite a lot of Russian-speaking Kurds; they live in parts of Armenia, although nowadays you can find them in Russia and among ex-Soviet communities in other countries too. There are even Russian-language Kurd internet forums, portals, news websites and so on. I think a lot of them are Ezidis (sp?), rather than Muslims as such. Anyway, they don't seem to have any problems in Armenia.