What would happen if Finland invaded Russia?
Finland just can't invade Russia. Impossible. The whole population there is less than the population of one St.Petersburg. Finnish territory is tiny compared to the majority of Russian regions. The army is very small and defensive rather than offensive. Finland has neither means nor purposes to attack Russia. Peace and friendship are waaaay more profitable for both.
And what happens if Russia invades Finland... well, it happened (Winter War, 1939–1940) and Russia lost, although annexed part of Karelia and the area of Vyborg (Viipuri), which Finns aren't keen to reclaim it.
If Russia decides to attack Finland now, which it won't, it will be a nuclear war, because Finland thinks on joining NATO (it's an ally to NATO members anyway, and member of the EU, EFTA, EDS, etc.). An offense towards any EU member is an offense towards all EU members, same as with NATO.
After WWII, the Finnish Army has been dedicated to defending only so it does not really have any tools to wage invasion against Russia. Russian army is not anymore any people's militia like it was in the Winter War but highly developed & technological high-end army and the amount of equipment & men Russia could throw against Finns would be unbearable.
Finnish army would suffer high casualties and be totally crushed in a few days.
The invasion would get its teeth kicked in and it'll raise Russia's nationalism and more nationalism is the last thing that's needed in this century. But I don't think the Russian's would get far in a counter invasion of Finland. They may have more manpower but the Finns know how to fight in their country.