I managed to solve this by changing both internet connections I was using to a third one. It seems the need for internet is much higher than both the internet subscriptions I was using were not enough at that moment.
So my advise: change the network in case something similar happens to a better speed one.
I do not know the reason, but last night the connection with the Simcity Buildit server was restored on all devices (via Blustacks too!) and everything works! In my village in the far Russian region there is no "third", fast network, there is only 3G and 4G with a speed of 8-15 Mbit/sec, but now everything is working well again. Thank you for your support!
