Did you mention where you live? (Good idea is to put general location and/or growing zone next to your name...) Yes, Sempervivums could be grown indoors but usually they don't look their best. I am not sure if they are better off with having to spend winter outside (some plants have to have x number of cold days to grow well); unless you get them really good light during winter they usually look quite sad. During summer it may not make that much difference. But amount of light is always less indoors than outdoors. But if you don't have access to garden or deck-balcony, you have to just do it indoors. Many ppl have to, living in apartments without balcony or any other outdoor space. All of the succulents need lots of light otherwise they stretch as I already mentioned about Painted lady. I use lots of supplemental lighting in winter, and probably will improve even more next winter. here is same Echeveria purpusorum, still indoors (March) and blooming, under lights: Adding more perlite definitely helps.

Severely etiolated...something in the Crassula family. Hard to tell. Give more light.

Chris Yes, pls. number them, take individual photos, or at least just 2-3 per photo. And try to get more of close-ups, some are very small to ID. Succulents need very similar care: fast draining potting mix, containers with drainage holes (hope all of yours have it), very good light - many will do best in good sunlight. And letting us know your general location or at least a growing zone would help. Best if added to your name.

Looking at the second picture, the two babies on the top are together so they count as one. Clockwise from the top, 1-4 with the haworthia being #2 :)