It is an Echeveria. Not sure on the type. It could be a Echeveria runyonii but there are a lot of E runyonnii forms and a lot of other Echeverias that look similar.

separating is easy. I cut them off. Sometimes if I pull them off the larger ones come off with a bit of root. I usually put them in a small pot of just rocks and I water or mist them. The rocks do not hold water but they create a moist atmosphere. I do this till there are a BUNCH of pink roots. Than I plant them in a a pot with a well drained mix.

So I can just cut the babies at the trunk of the mother, and even though they have no roots, they will re-root? I know many succulents have this ability, just wasn't sure if this was one of them...

All of the succulents i know of (maybe there is a few that dont, but i have never heard of any) reroot from cuttings. Echeveria in my experience is incredibly easy to reroot ... i took some leafs from and echeveria and stuck them in a corner and forgot about them, they sent out masses of roots and had plants growing out ... their roots traveled about 4 inches to a pile of dirt and grew into it, it was funny :D i wish i had taken a pic though...

I believe it is Echeveria secunda (previously E. glauca).

And yes, you can remove the pups and reroot them (easy) but I'd wait until The Pups were bigger - a larger plant is easier to reroot. Besides, the heat of summer is not the best time to root Crassulaceae (the Family your Echeveria is in), but it can be done.