A Few New Cacti

Here are a few new cacti I got. I would just like an ID and opinions on there health.

 

Pic. 1, fr. left, clockwise:
Parodia leninghausii
Euphorbia trigona (not a cactus)
Oreocereus (trollii?)
Stenocactus (most of them are difficult to identify on the species level), with fake flowers. They are usually white with dark pink stripes, or pale yellow.

Pic. 2 is not my kind of cacti, but the one on the right is probably a Myrtillocactus geometrizans.

They look healthy, but I would split the group in pic. 1.

 

Thanks thats really helpful. I looked up Euphorbia trigona on Wikipedia but im still not clear what kind of plant it is. Is it a succulent?

 

Oh yes. I have not owned one in many years, but here is some information.