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

You'd be surprised how many fake flowers are glued on to cacti...They're actually quite popular. I imagine the reason for not sticking a flower on the other cactus is because of its nasty looking spines. Lol. Lithops: Thanks! ^^ So, both are Notocacti? Eh...How 'bout Golden Ball cactus for the second?

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.

It looks like the San Pedro Cactus (Trichocereus pachanoi). It's kind of scarred and beat up, but I don't think it's necessarily sick. It appears that it may have scale insects, which may require a systemic insecticide. The white powdery stuff is mineral residue that builds up from watering the plant. cd