YEP. That's my guess too.Crassula 'Morgan's Beauty', a hybrid of C. falcata and C. mesembryanthemopsis. NIce plant.

That's Cotyledon orbiculata (there's a lot of variability in that species). You can repot it now - just wait several days after repotting before you water it. Teflon tape's great on pipe threads - not so much on plants. I don't think it will help it heal. Just remove it from the main plant. It will heal itself.

I brought mine in when temperatures outside dipped below 10C / 50F. Outside here in Canada it would turn into an icicle, but not sure how cold at your outdoor space? They grow better when it's cooler like in the fall. Summertime they are a bit slow for me. My plan is to keep mine growing well under lights until spring. Thanks!

This is not a very common plant in cultivation. You might be familiar with other types of crassula, often in unusual shapes and forms(ovata, arborescens, perforata, kimnachii, capitella,.....). While grass-like crassulas exist like yours, they are not cultivated as often, due to several species of sedum being way easier to grow.