Nice plants - can't help with the id. I have a gymno very much like that but still don't know what it is.

Jan

The Gymno should be a damsii or some ssp. of it.
The last one looks like a Coryphanta to me.

Alessandro

The Parodia might be sanguiniflora. Its flower color will determine its name I think. It does look very similar to mine, here in flower this summer.

Amy

{{gwi:493388}}

And without its bonnet:

{{gwi:493390}}