That's a tough one - many cacti, when they're small like yours, are difficult to ID. I can see it being a Gymnocalycium, a Melocactus, an Ancistrocactus, and a few other species, to a lesser degree. When it flowers / gets older and larger it will be able to be ID'd more easily. It looks healthy, so you may have to wait only another year or 10.

Misting succulents every week as a general advice is not very helpful -:( - not your fault but store employee. It needs to be in container with drainage holes (I can't tell if yours has them or not). It should be potted in fast draining mix - what I see looks like peat with very little perlite in it. Simple and better mix you can make is 50/50 mix of Cactus & Succulent soil and sifted/rinsed perlite. It should be watered when potting mix is almost completely dry - use bamboo skewer or chopstick to check it. It needs as much light as possible but should be acclimatized to it if it was in darker spot. This is what just about all succulents need.

Do the pots have drainage holes? If not, you need to take the plant out and replant in pots that have them or add them to this pot. Also regular potting soil often holds too much water for this type of succulent to remain healthy, so they will do best in a cactus mix or other sharply draining soil.

i see no reason why any houseplant cant go outside for summer... but in full shade ... but then.. as noted ... if there is no drain hole .... then you have to be careful about rain ... ken