Somewhy, in middle of me playing, all my units turn invisible so that I can't see them. Also my citys dont have anymore that bar which shows how long it takes until growth/production is finished...

it gets worse... I tried normal BtS and it has the same problem too...! I sometimes may accidentally click wrong buttons, does any of keyboard shortcuts or inside game buttons do something like this?

There should be one of the tiny buttons above the minimap to toggle those displays - otherwise Alt-I is the interface and I can't remember the terrain only shortcut. Alt-T ?