Brasilopuntia? Consolea (they all have at least two names each). It's certainly an Opuntia and from South America.

The 1st plant looks like Pedilanthus tithymaloides. Do a google search on how to care. You should find lots of infor.

The first one might be an Echinocereus. The lumps are probably buds that aborted and then continued to grow as pups. The Haworthia would like a bigger pot but don't go mad. You can take off the pups if you want more plants, or leave them if you like it as a clump. Old leaves do die off, but I find they die off quicker if you water too heavily or wait too long between watering. Its not a Ferocactus, don't water it twice a year with a hosepipe ;) Not sure what you mean by "non-soil". You mean peat? Not ideal for the Haworthia, not good at all for an Echinocereus. I use actual "soil", a sandy loam with added coarse material such as gravel, pumice, etc. Others use "non-soil" like coir, which seems to work well, or bark-based mixes which might not be so good. Check the roots when you repot, remove any which are dead and just keep the thick fleshy white ones.

Nice one Fred --- I think you tagged it...Thanks!....and I found a pretty cool site as a result of your answer. Copy and paste this [Doña Púa] into Google and the first site that comes up has some excellent photos/ids of some cactus: Doña Púa Lots of you vets probably know this one, but it was new to my eyes :-) The Mammillaria you id'ed is on the Doña Púa site too... Now I need to go back to that site and see if there were any succ pics/ids Thanks again Fred