A Sorry, we do not have statistics on the number of tourists in Minsk. I can count more then 15 hotels in Minsk. Three of them are rated as 3 star hotels. From my own understanding three more hotels provide the same level of services but are not rated. A Industry ownership.
All forms of ownership are present.
I know only one hotel owned by a foreign company. It is a small but comfortable German hotel Ursula. There are no private roads in Belarus. But there are some fees for using certain roads by foreigners and transit transport. Railway transport and infrastructure are owned by the state.