The trans Siberian takes 6.5 days to get from Moscow to Beijing. Thats the speed run, not getting off to look around. If you do get off you can be miles from where you actually want to go. Lake Baikal and the Gobi are skirted, but not thoroughly explored.
If you get off though, it might be up to 24 hours before another train comes through.
If you want to really get off the beaten track and ride on the BAM railway things get even more troublesome.
So without stopping anywhere this plan is going to kill 9-10 days of your trip. For that you are going to need a Russian and Chinese visa, which are pricey. Plus any other visas you need. Then you are going to try to fit 8 countries into the remaining 18 days?
I would consider doing just the trans Siberian, only in Russia, in 4 weeks. I wouldnt bother with China or Scandinavia on that trip, I would save those for another trip.