I don't think finishing everything on your plate would ever be deemed offensive in Russia. First time I hear about such a concept applied to Russian culture.
Leaving the food, on the other hand, is somewhat different. While it's not a general rule, some older people, especially those who survived harder times might see it as food being wasted. Just as often I witnessed people being upset that you haven't finished your portion because cooking might not be good enough for you. Honestly, if you encounter this mindset, it's hard to win unless you just eat A LOT. People would tend to try to convince you to taste everything available and eat as much as you can, and will get offended when you say "no please no more". It's kind of a stereotypical thing and while what I'm talking about might be a bit extreme, I've been in such situations more than once or twice.
The best strategy in shared platters environment is to take on the duty of taking your own food. Otherwise the host might think you're too shy and would keep giving you more until you're no longer able to stand up.
So, as a general rule, it's better to finish your portion than not. Look at others at your table and pick up the ques. Younger crowd is unlikely to care (but the most important is your host though).
As a foreigner, though, people will cut you some slack. Just praise the food and say "I wish I could eat more, I simply can't!"
With vodka - I think it's more of a lighthearted stereotype in that context. However, if you are in a company which has more than one bottle of vodka on a table (per <10 people, and maybe other alcohol), then it's better to feign some kind of disease, because it's likely they would make it their duty to make you dead drunk otherwise. I think it isn't really unique to Russia, among people using alcohol as their main entertainment fuel.