That is Rebutia krainziana

duwei

Mamm schumannii

Mammillaria heyderi.

Mamm. louisae?

1,2 Matucana madisonorum
3-M.bocasana
4M.nejapensis
5 M.backebergiana
6 Ech. reichenbashii most likely
7 Melocactus

All 3 IDs seem correct.

Large flower = grandiflora syn montana
Or something else

Hahniana woodsii may be?

Echinocereus mojavensis

Looks like some Rebutia, sure big enough to flower.

Can be quitensis. The bud usually has a barrel-shaped "base" that you can see if you google that name, but often it skips it and blooms directly off the pad and may then turn the tip of the pad into fruit. It is a bit of a biological wierdo.

Escobaria vivipara 1st plant. In AZ it is the most common cactus.

2nd looks like some sort of Stenocereus, but I can easily be wrong not seen flowers.

Most likely nickelsiae

Possibly Mammillaria tlalocii