Train types/compositions

[Marc87dk]

People here seem very friendly to help, so I hope you could answer this question. Considering how large Russia is, I am not even sure if this can be answered easily

Does the russian network have any specific categories that they sort the trains by?
Like in most european countries, they have InterCity, regional, etc.

I have noticed many overnight express trains have their own invidual names. How about the normal fast trains?
As an activity builder for MSTS, I would like to get the consists as accurate as possible. and there are so many cars and locomotives to download on this site, but I am not sure where they belong.

So what is the most normal composition for a normal fast train in Russia? (locomotive and cars)

All local and slow trains seems to be operated by EMU/DMU's as far as I have understood. Are there any "kupeiny" cars for local use?

I am sorry if this might be a bit of a tricky question