Austrocylindropuntia floccosa?

Acanthocereus tetragonus perhaps?

theheatherboo,
your first plant is indeed Mammillaria hahniana; the tilting is normal, nothing you can do about that.
The second one is E. grusonii, and I agree that the third one is an Espostoa. The brown on the wool is just dirt, again, nothing you can do about that.

I'm growing F. robustus from seed (my seedlings are about the same size as your plant) and that one looks very similar.

P. gounellei is the first name that came to my mind.

Pretty sure it is a cactus, some species of Ferocactus. The areoles are the wider parts on the ridges, the black dots are where the spines would be.

A very interesting topic!

I'm currently growing quite some melocactus species from seed (ranging from 1-5yrs), but I'm noticing they're very susceptible to spider mites. Was this your experience as well? I'm not quite sure what might be the cause...

If I feel like slicing up cacti I simply use a kitchen knife. You just need a knife that is sharp enough (and for seedlings, that means very sharp) not to crush too much plant-tissue.

Gymnocalycium baldianum

Because, as you stated, it doesn't look like a chrysacanthus. P. chrysacanthus is generally greener, has golden spines, has a slightly different growth habit (hard to put a finger on that), ...

2) a Lobivia I think (lumped under Echinopsis now?)
3) M. karwinskiana

P. pachycladus indeed. P. azureus is now conisidered P. pachycladus, but the name is still often used.

Hah, whilst the second one isn't an echinocactus, indeed; they're only endangered in their native habitat (i.e. in the 'wild'). They're by far the most cultivated cacti (except for those Gymnocalycium grafts maybe...). I'm pretty sure your second plant is a Parodia, either P. magnifica or P. warassi...

Pretty sure the second ones are Agave, the seeds (you can see some in the pot) look very Agave-ish.

yes, I agree with both