After taking the trip, for the future generations coming here from Google ...:
For the flight Europe-MSQEurope–MSQ, one does cross the bordergoes through immigration in Belarus (as expected) and gets an entry stamp. Single-entry visa is accepted in this case. Visa-free regime cannot be used, as the next destination is Russia.
For the flight MSQ-LEDMSQ–LED, one does not cross the border inpass Belarus exit immigration, but does go through entry immigration in Russia. This means no exit stamp from Belarus and an entry stamp in Russia.
For the flight LED-MSQLED–MSQ, one does cross the bordergoes through exit immigration in Russia, but does not go through immigration in Minsk. This means an exit stamp from Russia, but no entry stamp in Belarus. No any check takes place in Minsk; one leaves the plane directly to the non-secure zone of the airport.
At this moment please do note the state of entry/exit stamps - Russian part is clear (both entry and exit stamps), but so far the traveller has never got the Belarusian exit stamp.
- For the flight MSQ-Europe, one crosses the border in Belarus, but the dates do not match at this moment - visa was valid only till the day of the flight to Russia, whereas the border is crossed at the day of the flight back to the Europe. This raises the questions and the real date of leaving Belarus has to be proven with the boarding pass MSQ-LEDMSQ–LED.
The Belarusian exit stamp is given with the current date, what causes the dates from stamps and visa not matching each other. Every trip to Belarus will require explaining this situation.
Just please note, none of this has caused any inconveniences. This is just a very unusual route for the foreigner and as such, has to be handled manually.