Considering that most if not all Europe to Asia flights go over Russia, it will be awfully long escorts and Russia will 10x cost too. Besides that Russia has nothing to do with current incident.
Of course they do, Belarus is in their pocket and they have to pay accordingly. NATO cannot display weakness again and again. If Russia increases the fee then we take away their planes (via maintenance) which pretty much bans them from travelling around the globe.
It would be expensive to divert for Japan and Korea, not so much SE Asia. I can't see Russia fucking with China though.
Flights already do a big detour around Ukraine because of their conflict with Russia. In fact, middle eastern hubs would love Belarus airspace to be restricted, it makes their routes much more competitive. Flights to SE Asia often fly further south, over the caucuses, Afg/Iran to SNG, or Iraq/Iran to Qatar since the GCC blockade. (Iran charges considerable fees for this btw, a good source of hard currency.)
I'm afraid Russia has everything to do with this incident. There is no way they would do this without Putin's okay. That he is willing to risk Russian airspace rights shows how desperately worried he is about popular uprisings.
The ops.group newsletter [0] is a great resource for understanding flight restrictions.
