What is necessary to work with inset face mode? I'm trying to inset another face near the center of this plate. After pressing I key the inset information appears on top of the screen but there is no dotted circle showing the preview before confirming and no additional vertices are created after confirming.

I have tried to reset scale using Ctrl+ A in Edit mode and Object mode as other answers suggests but it didn't work. Also closing blender doesn't seem to solve the problem.

I have 3rd mouse button emulation enabled.
In your image I can see that you are using Vertex Select. In this case, activate Face Select.



Inset Faces is a Face Tool. It needs you to select all the vertices/edges that make up a face.

You can use it via Vertex Select (or Edge Select) as well, however, you need to select the central vertex to select the tris (triangles or faces with 3 vertices).