Till the end of the season 2, it isn't stated or hinted that he is a Russian spy. It's just fan theories. He could be, but this part is pure speculation for now.
However, the points you refer really don't hint that he is a Russian spy. To explain it better, I will go through all points one by one.
- The S2E6's name is The Spy.
This episode title is not really referring to him, but the Shadow Monster. Since it is inside the mind of Will Byers, both can see through each other's mind which means that both can spy on each other. When Will tells about the shadow monster to Mike, Mike asks if he can spy on it.
Mike: Good? Just think about it, Will. You're like a spy now. A superspy. Spying on the shadow monster. If you know what he's seeing and feeling maybe that's how we can stop him. Maybe all of this is happening for a reason.
Will: You really think so?
Mike: Yeah. Yeah, I really do.
Will: What if he figures out we're spying on him? - What if he spies back?
And that's exactly what happens in the next episode.
Will: They upset him. They shouldn't have done that. They shouldn't have upset him.
Mike: The Spy. The Spy!
So, it's clear that the title is not referring to Murray, but the shadow monster.
- Murray stores and drinks lots of Vodkas.
Vodka is a popular drink across the world, which was originated from Russia. However, it is available in many countries, and there is no such rule that only Russian can drink vodka. Therefore, him drinking lots of vodka doesn't really make him a Russian spy.
- He doesn't want Nancy and Jonathan to reach him again.
Well, he is a detective and doing his work to find Barb (Nancy's friend). Detective work requires a lot of focus and it should be done very quietly. If Jonathan and Nancy try to contact him again, he'd not be able to focus on his work.
After going into details of all these points, these really don't hint or prove that he is a Russian spy.