It's an Echeveria of some kind.
It's stretching because it badly needs more light. They should stay a compact rosette if given the proper amount of light. Echies especially like to have a lot of light. They stretch really fast if there isn't enough.
Also, does the pot have a drainage hole in it? Succulents need to be potted in a fast draining soil mix, and in a container with a drainage hole. They'll rot very fast if the excess water can't escape, or if the soil holds water for too long.
It is normal for the lower leaves on Echies to die off over time. New ones will continue to grow to replace them.
