No matter what mix it's in it doesn't change a plants cultivate. It's an Echerveria of some type and would agree that it's a very special and might be a rather unique cultivate too. Perhaps it's Echerveria Sub.Sp A little overpotted Cv. Wont fair well in mud ?

The pot isn't really too small (could repot into just a bit bigger), but the plant sits too low inside of it - needs more 'soil'. All succulents (regardless the name) need good drainage, plenty of light and good air circulation. You could grow it inside, but need to give it as much light as possible, most of the times there isn't sufficient light for succulents (they will live & grow, but likely will etiolate because of not enough light). I believe that's original soil - it will be best to repot into much better draining potting mix. I see some yellowing leaves & that could be sign of waterlogging, & may cause rotting. Rosette type succulents grow leaves from the center. It could be one of the Echeveria agavoides.

They look like Echeverias, which prefer very mild conditions, neither too hot nor too cold, 18C - 25C is ideal . They also do not like hot, humid conditions. They can take heat but not humid heat. Plant in a gritty mix, keep water off the foliage, water sparingly. A few hours of direct early morning sun (before 10 am) followed by shade. In rainy weather keep them dry.

I do not know exact name, but the cactus you have needs to be planted in well draining mix. It seems to be in dense soil now. Fast and easy mix could be made by using lots of perlite with the soil, at least half of the total volume. I am assuming the container has a drainage hole?