The last one might be Mammillaria vetula ssp gracilis. The first might be a species of Gymnocalycium.

I think the first one will be Sulcorebutia.

First one is Rebutia arenacea, second one could be a Rebutia as well, but also possibly an Eriosyce species.... last is indeed a Mammillaria, but Mammillaria theresae, not gracilis.

p.s. all Sulcorebutias have been sunk into the genus Rebutia... that first one was a Sulcorebutia at one time.