It looks like bug bites.

Temperatures here in Tennessee drop below freezing REGULARLY and CONSISTENTLY in the winter. Therefore, all of my plants--cacti, caudiciforms, succulents and ONE ficus tree--stay inside for the winter. it will be much easier to back off the fertilization ( one in three waterings do you think ? it i...

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Those haworthia seeds probably need more time. I sow several cacti/succulent species every year, and this year I've sown haworthias among others for the first time (3 different species), and I've noticed they take longer to start germinating than cacti. Mine took 3 weeks to start germinating, I was ...

Use a knife or cutter to avoid ripping the core out.
Rooting the cutting should be easy, let the wound callous (1-2 weeks), and then pot it. No direct sunlight until it grows new roots (you'll notice new growth on the plant).

Put the pot in a bucket and fill the bucket with water until it covers the whole pot (up to the base of the plants) and leave it there for 1-2 hours.

The one marked as Echinopsis peruviana is not a peruviana, and "cutting 3" looks like myrtillocactus geometrizans.

Nice garden.
How deep are those beds?

5-8 -> Echinopsis chamaecereus, Mammillaria elongata, Cylindropuntia subulata monstruosa
13 -> Opuntia monacantha

cactus 1 - Cylindropuntia cristata??
cactus 6 - Cereus jamacaru monstruoso.
cactus 7 - Opuntia mycrodasys albispina (bunny ears), some variaty of Aporocactus??, echinopsis huascha??
cactus 8 - Mammillaria elongata.

I'd say second one is a Cereus jamacaru monstruoso.

I think it is not a cactus, it looks like Euphorbia ingens.

Your "tall and spiky guy" is a Mammillaria elongata, and the monstrose one is an Opuntia monacantha monstruosa variegata .

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The right one is Opuntia monacantha monstruosa variegata and left one looks like Euphorbia horrida.