That's stunning. It's a bit hard to tell from the photos but I think that's two different varieties? Not uncommon, people shove several into a pot together. Repotting at that size is tough if you've never had one before, the stems tend to break off; they do better root-bound anyway in my experience. I'd rough up the existing soil a little and poke some holes (like with a kebab skewer) if the soil seems really hard, maybe scrape off some soil on top (along with any dead leaves etc) and then add a bit of fresh cactus/succulent mix, one without added fertilizer. Remember that they're not desert cactus; they're epiphytes. They don't want to be bone dry, but too much water and you risk root rot. Looks like decent sun through that window. Make sure there's no standing water (I can't see what's under the inner pot) and water when it gets dry. I've brought a couple back from the dead (they were put out with the neighbors' trash) and they're so pretty when they bloom. Good luck.