The worst part about using unglazed ceramic pots is when you come to repot your plants in them and you have to rip off so much root tissue which is stuck right to the side of the pots as the plant has tried to root into the clay. Sure they help plants to dry out faster, but if your plants are health...

Did you get your plant from David Quail (Aristocacti)? I've heard from others that some of his plants suffer from Magnesium deficiency, since he grows these slow growing types in seed trays for the first few years. Perhaps adding a little epsom salts to your next watering would be beneficial. Howeve...

They're all a bit etiolated and would benefit from more light.
1. Mammillaria polythele
2. Euphorbia enopla
3. Cleistocactus strausii

A monstrose Eriosyce of some kind. Maybe the one usually sold as Neochilenia cv 'China Wonders'.

The plants themselves look healthy, but that will soon change if you don't get them out of that terrible looking soil mix. Repot into a mix with far less organic matter.

I know an English-speaker who lives in San Pedro de Atacama. I would love to visit some day. Touring the entirety of Chile would be awesome.

I've bought lots of cacti on ebay in the UK over the past three years and haven't yet had a bad experience. If you look at the individual feedback comments on a seller's rating, you get a feel for the reliable sellers. Good call, I have had some very nice plants from uk ebay sellers. As have I, but...

Probably rot. Doesn't sound healthy whatever happened to it.

Echinopsis spachiana and Pilosocereus pachycladus are my guesses.

Sulcorebutia arenacea, I guess.

I disagree, looks like Carnegiea gigantea - Saguaro. E. grusonii seedlings are stouter and have a different aerole structure.

There is a subforum specifically for cactus identification. More people would see probably your post there. The smaller plant in the pot is Stenocereus pruinosus, but I'm not sure what the big one is.

Mammillaria schiedeana.

Here's another one. Copiapoa hypogaea ssp tenuissima. Odd question for you, Ian -- when you transplant cacti, do you center them in the pot? My reason for asking is that I'm pretty good at centering mine, and I notice that a number of them go through "continental drift" as their root grow...

They look good!