Earlier quoted context omitted.
No, Russia buys it for a song (since they're the only customer) and uses it domestically and possibly sells it along to Europe. I've certainly never heard of the Turkmen gas being unusable for regular purposes. There's a small pipeline to Afghanistan that supplies the border regions (when its running).
this is incorrect, there is a direct pipeline from Turkmenistan to China who buys about 6x more gas from Turkmenistan than Russia.
You are correct. I wasn't up to date on my Turkmen pipelines. I'm sure the Turkmen would be more than happy to sell to Europe though.