The cactus in the center of the OP's first photo is Cereus forbesii forma monstrosus 'Ming Thing', a monstrose, dwarf form of an arborescent cactus native to Bolivia, Paraguay, and northern Argentina. There has been a taxonomic debate whether the correct name for the species is Cereus forbesii or Cereus hankeanus, so you may find this plant to be listed under either name.
...and yes, there is also a Mammillaria sp. in the first shot.
The cactus in the OP's second photo is an Austrocylindropuntia sp., possibly A. cylindrica. The genus is native to Colombia, Ecuador, Peru, Bolivia, and northwestern Argentina