So to me it seems like the US could have its entire army at a base in
Finland and Russia could still sleep in peace. What is wrong with my
For the record, I think you're mostly spot on here. Russia has very little worry of a US/Nato invasion. The US/Nato has no interest in a war with Russia. It would be ugly and expensive and as a US citizen, US war fatigue is well documented. People wants us to get out of Afganistan and Iraq, not get involved in something new. Russia knows this. Russia knows that Nato doesn't want to attack.
But that's only 90% of the equation. For recent conflicts in Ukraine and Georgia, after those nations were part of the USSR for a time, there were Russian relatives on the other side of the Ukraine and Georgian borders, especially in Western Ukraine, Crimea, Abkhazia and South Ossetia and there was conflict within those nations between pro Russian and anti Russian factions. It makes a difference how a nation leans for international trade and there was some infighting within those nations that were formerly of the USSR. Russia wanting to protect their people and annex some parts of those nations could be argued as in their self interest beyond reasons of just wanting a "buffer region".
A 3rd issue is oil and shipping routes. Russia's involvement in Syria makes it harder for middle east nations to run a natural gas pipeline to Europe. This increases Russia's natural gas monopoly. They're a stones throw away from the pipeline that travels through Georgia now too and they have a stronger naval presence in the Black Sea and with Syria, the Mediterranean as well. Even if the fear of attack is low, having a stronger military presence can be appealing.
In the future, oil drilling in the arctic (and perhaps antarctic), but the Arctic border's Russia. As ice melts and shipping becomes easier and at some point, oil drilling in the arctic ocean will probably increase, Having a strong military will benefit Russia.
As far as the Moon in Russia - what I've read about it, their citizens are generally happy about the military advances. Russia is in an economic downturn with the price of oil being quite low for the last several years. Having a strong military makes them feel more significant. (I've heard experts say exactly that when being interviewed - I'll try to find a source) and unlike America, their population doesn't suffer from war fatigue. That doesn't mean they want war with Nato, only that they don't mind and even appreciate, military expansion, at least on average. You can always find individuals on either side.
So you are right, they have very little to fear from a Nato attack, but they have reasons to want to expand their borders. The "Buffer zone" isn't primary among their reasons, but it's a convenient excuse.
And while war is, I would think, unlikely, and the arctic ocean is already divided, some military posturing over who can do what in the arctic isn't out of the question and having a strong military behind them never hurts when negotiating.
There's also a small chance that war could break out, and even if Nato doesn't think they "started it", if war happens, Russia will be grateful for the buffer nations they have.
I feel that I should point out that there's two ways Russia could have gone. Working with the west, increased trade, building an economy and maintaining friendship. They tried that for a few years but their economy never took off. Russia was seeing former states that had been under their control surpassing them economically. The 2nd option was basically what Putin did. Take stuff. Taking stuff isn't out of fear of Nato, it's out of wanting stuff. I want that, lets take it. Oh, and lets build more tanks in case they try to take it back. Putin's answer is "We're defending ourselves, Nato is aggressively expanding". he's, contrary to what people may think about him, very smooth.