Also https://www.bennyskaktus.dk/Hardy_UK.htm

I don't think that's E. oxygona. The flower is too small, a bit too ivory-coloured, the throat is too narrow and the petals too abruptly reflexed. I reckon it's a hybrid but not one good enough to name. It's the sort of thing you might get if one of your species plants set a fruit but you didn't kno...

This is correctly identified. If you've pulled pups off your plant it probably isn't an Oroya: are you sure you don't have a Matucana?

schickendantzii was my first thought.

Pachycereus marginatus?

Some back numbers: https://cactuspro.com/biblio/en:cactusaventures

Given how easily it sets seed I think it's self-fertile. The only time I sowed the seeds they came true.

Looks to be canigueralii.

Re Turbinicarpus Aioinopsis asked about. I note Joel's remark in my last link above:- "In August 2019, a new molecular study (Vázquez-Sánchez et al.) confirmed that Turbinicarpus should be split into three genera: Turbinicarpus sensu stricto, Rapicactus and Kadenicarpus, already suggested in T...

OK, yes, that makes a difference! Borzicactus icosagonus (aka Cleistocactus, Seticereus)

Haageocereus, perhaps H. pseudomelanostele.

2 & 4 are O. robusta.

Cumulopuntia leucophaea (or C. sphaerica if you prefer).

Need to see flowers really - get back to us in November.