I made a character and rigged it manually, and skinned, and everything worked fine, and then I wanted to add some shape keys for the face, and not make face rig because I don’t need it for this occasion, but when I added basic shape key and two more, mesh stopped responding to rig commands. I checked, and everything is skinned as it was. Does it matters that I added basic shape after all the skinning and can I repair that somehow? Other meshes that are part of the rig but separate objects are not affected, work normally.
Without a blend, I can only guess that you have some obscure setting messed up or enable that should not be. Adding shapekeys should not effect your skinning, parenting, or weighting. Did you disable the armature modifier on your main mesh? (Eye icon should be on.)
Show us a screen grab of your mesh’s modifier stack or upload a blend. (Use pasteall.org.)
I was parenting some things after that, it is possible that I messed up something there. Reverted to earlier file, repeated and it worked just fine after that.