Why doesn't Russia join NATO and what would happen if it tried?

So, I'm likely demonstrating my own stupidity here, but I'm wondering what I'm missing.

Russia claims that it's afraid of NATO and feels like it might attack it. So... what if it joined NATO? I know, Russia's like the last country on the planet that would join, because NATO practically exists as a counterpoint to Russia... but hypothetically, if Russia also joined, what then? Wouldn't it be safer for Russia that way? It would have access to all the inside knowledge of NATO, and it would make much less sense for any NATO country (or NATO as a whole) to attack Russia because... well, they're on the same side now. Right?

I suppose there might be strings attached and obligations that Russia would need to fulfil, which they are not willing to do, but what are they?

And on the other hand - if Russia suddenly appeared out of the blue on NATO's doorstep and asked to join - would it be accepted? Or would other NATO countries be too distrustful of Russia to allow that to happen?