I've mixed thoughts refferacing the inner and outer ceramic glazing of the coffee cup. they work but drilled drainage " holes on the bottom " may need to be increased ? or more. It's a bit wet now and entire plant and roots should come out easy for you, set the entire soil and plant on news paper with news paper on a tray allowing some dry time ( over night) as you prep the looser (airy) suggested soil. Watering may take time for you ( climate area, air ect..) to get use to. Size of it and seeming that you might want to to but will ask Are you indoor window sill growing all season ?

Yellowing of leaves is usually caused by overwatering - plant being in water retaining soil. White particles are most likely perlite; is it is same material as blue particles - I believe it is perlite discolored by excess amount of fertilizer. Pick white & blue particle, feel them, even try to squish to see if they fall apart the same way - you can tell then if it is same material. Perlite is good, there should be much more of it, but excess fertilizer is not beneficial. I would get all of the soil off the roots, try to shake it off, help yourself with a chopstick or bamboo skewer to pick it/loosen up from the roots. If some still remains & you can't get it off, swish roots gently in a bowl of tepid water & hopefully it will soften up. Let is dry off on some newspaper or paper towel, check the roots. If any are dry or damaged or mushy/dark looking and slimey, cut them off. If you have to make few cuts, you could dust lightly with some powdered cinnamon (not absolutely necessary, but cinnamon is a natural fungicide); then repot into well draining mix in a container with drainage holes, that is not too large. Make sure you put enough mix into the new pot so your plant doesn't sit too deep in the pot. Leave the pot in little shade for plant to recover and don't water for few days - if you had to wash the roots, there is likely plenty of moisture available. If you had to cut most of the roots (or all), do not water until you see sign of new growth. Should plant be 'wobbly' in the new mix, you could support it with few stones or rocks, or a layer of grit as a topdressing. I would get rid of all old soil, good to put in a compost heap.

I don't think succulent rot usually presents itself in dried up leaves. In my experience, it's usually shriveled leaves that rapidly turn yellow and fall off, and a blackening stem. Also, the placement of the dried leaves isn't starting from the bottom of the stem and working upwards, it's in the leaves that are exposed to sunlight. So, I don't think you need to worry about rot. Looks like these guys are shocked and sunburned from the sudden change in environment. Succulents need time to adjust to bright, direct sunlight, especially when you buy them from a store that keeps them indoors where they're getting little to no sun. Gradually give them more and more sun each day for 2 weeks until they're properly acclimated to the amount of sun you'd like to give them everyday. The change in temperature from a cool air-conditioned house to a warm/hot outside could also have contributed to this blanched appearance. Overall I think your semps look pretty healthy, other than the dried bits! You can probably just pluck those leaves off, if they bother you.

Your sempervivum looks OK, only a bit lacking in light. They can be grown indoors but they need a lot of sun. Your semp has flowered and you are seeing a normal flower stalk. The main plant will now die, leaving the pups around it to continue the plant. You should cut the pups off and let them root as separate plants and repot one back into the pot, otherwise you are going to be left with a gap in the pot and the pups hanging outside. The other one is an echevaria and also showing a litlle lack of light. You can cut the top off it, let it heal for a week and reroot it before planting it back into the pot. Otherwise it will have a long stalk with leaves at the top from now on. Give them as much sun as you can from now on.