Why my Bevel move verticies along the edges instead of bevel them? At one side Bevel works perfectly, but with similar edge on another side is a mess.
The same problem with another edges. Bevel goes flat, verticies run along the edges.
I have no doubled verticies. Recalculating normals for all this verticies didn't helped. I have no inner faces. There are edges between all this verticies.
It was caused by one flipped face.

The Bevel tool was confused, not knowing which way to go.
Recalculate Normals, so they're all pointing outwards.
Then the Bevel tool will work correctly.  

Mesh > Normals > Recalculate Outside