Plants in 1st photo are potted in glass dish/bowl...does it have drainage? That would be big problem for your succulents. 2nd plant will not 'recover' - meaning rubbed off powdery coating (often referred to as farina) is not coming back. It will be on new leaves, and try to handle plant by the leaves as little as possible. Farina is there for a reason: it protects leaves. Lack of it may not be so important in potted plants at home, but they will look 'different' as you found. Can't tell what the plants in glass container are potted in, but 2nd looks like very peaty mix. It would do better in fast draining mix, potted little higher in the pot (seems to be too deep/low now). Your succulent plants should all be in fast draining mix, in containers with drainage holes and should receive plenty of good light.

I think 2 is actually Euphorbia x japonica. Not sure about 1, but it's also a Euphorbia as Rina said.

Dry and shriveled is good, yellow and soggy is bad. Your Haworthia is doing what it should and that’s using the old for the new. If I could make a recommendation;). The mix looks hard and dry so it would be a good idea to switch the mix to something that is more succulent friendly;). An easy cheap mix is 50% perlite or pumice and 50% cactus mix. The mix it’s in now is what peat based soil looks like when it’s dried out, it becomes hydrophobic and really difficult to get water to the roots. Lastly, the pot should have drainage holes.

I'm not an expert so anyone else feel free to correct me. Usually purchased succulents need to be repotted with a faster draining potting mix. Most often recommended here is commercial cactus/succulent mix combined 50/50 with perlite or (preferably) pumice if available. The pumice or perlite should be rinsed in a screen to wash out tiniest particles. Probably the pot it is in is a good size unless it is root bound. Then you could size up but only to a pot with hole in the bottom. Remove as much of the peaty mix from the roots, you can even rinse it off. Don't water for a day or so after repotting. Best not to double pot as you purchased it. Single pot allows more air circulation around the pot and less humid conditions. It's a nice plant. You will enjoy it for a long time. I'm not sure of the light requirements, but probably good bright light at the least, maybe some direct sun.