Yes, it is Paulownia tomentosa, a non-native invasive weed tree. Here is a link that might be useful: North Carolina invasive plants

Looks to me like, top-left, Echeveria 'Doris Taylor'; upper-right, Echeveria runyonii 'Topsy Turvy'; and lower-right, Aeonium 'Kiwi.' I don't grow many cacti and don't pay much attention to IDs for them, so someone else I'm sure will chime in for that one. This post was edited by teatree on Wed, Apr 17, 13 at 21:22

You can either do a leaf or the top bit of stem (maybe three inches) let it callus over a few days, lay it on some dry medium and roots will grow. Then,it can be planted up, wait a few days and go ahead and treat it normally. A leaf will grow a small plantlet and so it's the longer way to go. The bottom of the stem (the super stretched one,I'd get rid of the middle bit) so like the bottom inch or two that's rooted will likely start off shoots. BUT they all have to be put into much better soil/media. Everyone here has different mixes but a good rule of thumb and the easiest fix is to add perlite to the cactus soil you have at a 50/50 ratio. I personally like decomposed granite and pumice but really it's just a matter of breaking up the soil so water drains quickly and air can circulate around the roots. Which, incidentally will not work without drainage in the pot so make sure there are holes. If you Google "succulent propagation" you'll get some great how tos with pictures and step by steps.

Spraying succulents isn't such great idea...they need to be watered when potting mix is almost dry, thoroughly. Then they should be left alone until mix dries up again. Watering in 'sips' or spraying is not for succulents. Sempervivums are hardy, Alpine plants. Should be grown outdoors year round, in containers or in ground. They do not need 'rich' soil, should be in well draining mix just as any succulents.