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.

Pagan - Is it me or they require an absurdly high amount of light to stay compact? It's a bit off topic from the original post, but I can get mine to colour nicely but not that easy to keep them looking 'perfect'. Maybe I should start a separate thread...

Ah yes! Very important. Gradually over 2 weeks, to prevent sunburn.

The stem has rotted including the growth point at the top. You can dig it up and try to look at how much of the stem is rotten and try cutting off the rotten parts. You might try picking off some leaves that don't have any rot and try using them to start new plants. That looks like an Echeveria. They will easily produce a new growth point from healthy tissue.