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.

As rina said, I would take it out and add more soil, so that more of the leaves sit above the lip of the pot. The lower they are in the pot, the greater chance it is that they will rot because of decreased air flow and water sitting on the leaves.