The species is not "fulviceps" but Eriocactus or Parodia claviceps. As said before claviceps means club shaped, whereas fulviceps would mean dull brownish-yellow or tawny headed. Your plant is obviously not neglected but growing very well. Here are my Eriocacti (Parodia) Left back E, wara...

For the second one I could suggest Eriosyce crispa var.huascensis

Mammillaria bombycina and Mammillaria microhelia

They both look similar and I could suggest Parodia (Notocactus) ottonis cultivar militaris

Second - Notocactus (Parodia) buiningii, third one - Ferocactus glaucescens

It looks like Eriosyce (Neoporteria) senilis. My avatar is actually its photo in bloom

I can suggest some IDs. Although it is not encouraged by the Forum to post 20+ plants for identification. 2-3 in one post would be more appropriate 6 - Stenocactus (Echinofossulocactus) lloydii 7- Discocactus sp. 8 - Mammillaria, possibly from magnimamma group 10 - Gymnocalycium saglionis or pflanzi...

My suggestions would be:

1, Echinocactus grusonii
2 Parodia leninghausii
5 Gymnocalycium (from anisitsii group) it will be easier to tell when you see the flowers
6. Hamatocactus hamatacanthus

Harrisia martinii IMHO

I believe it is E.oxygona http://www.llifle.com/Encyclopedia/CACTI/Family/Cactaceae/8376/Echinopsis_oxygona Subdenudata is spineless, or almost spineless, and its flowers have more slender stems compare to Easter Lily Cactus http://www.llifle.com/Encyclopedia/CACTI/Family/Cactaceae/17377/Echinopsis_...

Definitely not grahamii, which has more prominent spines and especially flowers. M.crinita seems like a match. the one with pink flowers possibly is M.crinita ssp,zeilmanniana

I could suggest Notocactus horstii for the second one

Mammillaria microhelia would be my guess

Thank you Nona, I think it is a match!

It is a possibility I think. It is in 3" sq.pot. Thank you for the suggestion!