"""""One more problem with circles.
Why do I get those unsmooth edges?.
And why is the curve smooth and the geometry inside is shown not smooth?"""""

Michael explained it, but....

You can set options-view-mesh angle to a lower value and get better results. Put 4 then look again.

Larger models will start to slow down. :o

So maybe dont "keep" it low... just use it to "check"