That looks like a slightly etiolated Graptopetalum paraguayense (or a relative hybrid). More direct sun (as much as you can give it) would improve its legginess - you can also cut the stems and reroot the cuttings - plant them in the porous soil (what you're using appears OK) and mist them only until you see new growth, when you can start watering them.

I actually recently moved it from a north facing window sill to a south facing window because I had a feeling it would like more sun. It seems the stems started drooping after the move, but that could be because it's grown more?

So where should I cut the stems? Closer to the soil or closer to the leaves? Do I need to leave the cuttings out to grow roots or can I immediately plant them in soil after I cut? Also, do I need to dig up the old stems that are already rooted, or will they grow leaves eventually if I leave them planted?

Also, what are the little hairs that are on the stems? Sorry for the 20 questions, I've had this little plant for a few years now so I'm excited to figure out how make it prettier and maybe a little fuller.

Crystal,

Yes, it's time for it to grow. You can cut the stems near the base. Let them dry for a few days (the cut will callous) and then plant them. Those little hairs are adventitious roots (see the thread on 'Aerial Roots' at this Forum for more information).