Root mealies - yikes! Definitely need to kill off those.

Otherwise, looks good. Plenty clean enough, retained lots of roots - in fact, I think you need to trim some of the really long roots.

The ones that are struggling may perk up when you get them in a better medium, wish you luck.

You want the old leaves to dry up first - no water yet.

Yes, you should get them out of that stuff. When it's warm enough for them to take water (might be now where you are), I would soak them in warm water a few hours or even overnight to soften up that mix. A bit of soap in the water as a wetting agent could help.Then you should be able to separate the...

No surprise - offsets sometime grow roots even when they're above the soil line, those that are below the soil usually produce their own roots. That thing's ready to grow - I'll bet it starts showing some green even before you plant it.

It has dried-up flowers on it, so it clearly does bloom - just need to be there in the blooming season, probably late spring. S. steinbachii looks likely to me.

It lacks chlorophyll because it wasn't getting any light. It should do fine, but be careful about sunburn until it's fully greened up.

What's your biggest A. myriostgma? You've got some real monsters, I had no idea they could even get that big!

It happens sometimes when the growth point gets damaged, or when growth is interrupted somehow.

A very nice G. mihanovichii.

Seems like every cactus sold on Ebay is "rare".

In either case, woolly cacti need strong light if they are to stay woolly. Introduce it to the sun gradually, it could easily sunburn in this condition.

I think it's M. bocasana - the central spines are brown, though you have to look very closely to see it.

I agree on the ID. There are many different monstrose strains of this species, there's a lot of variation. Some remain quite compact, they produce tons of offsets and grow into a blob, others can get really big - and there's everything in between. This looks to be an in between one, so it's hard to ...

Looks like M. plumosa to me...probably.

No cactus produces a blue pigment, Those that appear blue have a waxy "bloom" on their surface that scatters light, and short-wavelength blue light is scattered more than other colors. Gymnos don't produce a waxy coating.

Seems to be a fairly variable species. I'd say close enough.