Usually one have to deal with a landlord in person and find a landlord by oneself
It's the same in Latvia too. I did not even consider state-owned flats and started searching in classified ads immediately.

Now I'm renting a two-roomed flat with my sister in Minsk for 400$ per month
That looks expensive - is it in city center?

My rent for one-room flat is about 120$. (near city center)
I finished university this year and I should work for two years where government says.
I finished about a year ago and did not have to pay anything.
There are two ways (in state owned universities) - either you pay full price - or pay nothing - if you have good enough exam results (government pays for everything).
So if you are smart enough you can graduate and not be in a gigantic debt like many american students.

They should not have allowed that to happen and it's understandable that people are upset about it.
They raised wages before "elections" to the levels that were unsustainable in long term - it is unsurprising that they had to devalue.