Hi Mercedes,
As it happens, I visited a friend yesterday who has a form of Thelocactus tulensis that looks a lot like your #2.
It is from La Hincada SLP, I believe the field number is L-1311.
But, there is also a species found in La Hincada under the names T.flavus and T. panarottoanus which also looks a lot like yours.
Supposing it is a Thelocactus, if you follow the Cacti Guide taxonomy T. flavus is placed as a synonym under T. tulensis which would mean that Daiv was both ways right. Other taxonomies place it under T. conothelos as a subspecies.
The most obvious difference would be that the flowers of T.tulensis are white to pink, T.flavus etc would be yellow.
Gr. L.
#1 looks Rebutia to me rather than Parodia. I have no idea what species though. I have just started growing Rebutias from seeds. I will tell you if it gets similar to yours (in about 2-3 years or so ).
I would have also said Rebutia (minuscula?) for #1 except that the flowers look like they're coming from near the apex. Don't Rebutia flowers generally start from low around the sides of the plant?
In the enlarged genus Rebutia there are plants that flower from the base or from the apex. The one that flower from the base have been called Rebutia, Sulcorebutia, Aylostera, and Mediolobivia. The ones that flower from the apex have been called Weingartia. The divisions between them all have been argued over ever since they were first named. Strangely enough, Sulcorebutia and Weingartia appear to form a single inseparable group, and according to recent DNA studies it is a group not closely related to the others.
Weingartia flowers are mostly yellow, occasionally orange, and rarely what you might call red. The red flowered plants don't look like this. In any case, the flower shape is wrong and looks much more like Parodia haselbergii.