You're right (and now I wonder if my own Mammillaria spinosissima aren't mislabeled).

1, 2, and 3 are different cultivars of jade plants (Crassula).

The fourth is an Echeveria which appears to need more intense sun and less water than it has received.

Most Euphorbia trigona plants don't have red leaves.

The first is Mammillaria hahniana and the second looks like a Mammillaria spinosissima that doesn't have spines. There are a few cultivars which do not have spines, or have minimal spines.

Are you sure it's glued on?

This type of flower is sometimes pierced into the stem of the plant, like this:
And sometimes they are both glued and pierced at the same time. It really does ruin some plants.

I have only grafted a few Mammillarias but in my experience the milky sap doesn't affect things one way or another.

Has it a white sap when cut?

It looks like a Euphorbia trigonus, which is not technically a cactus.

How much has rotted? If any part of it is still firm and healthy, you can always cut back to that and try to re-root the cutting. This doesn't work with Gymnocalyciums the way it does with columnar cactus, in my experience. Due to the globe shape of Gymnocalyciums there is nothing or little to cut ...

If it has actually started to rot there's nothing you can do except maybe take an areoles cutting and graft it.

If rot has set in, no amount of drying or antifungal will help--it's too late.

A picture would always help.

Is the Gymnocalycium soft? It looks squishy.

Yep. The leaves of Aeoniums are shaped differently than those of Echeverias. They also have different care needs since they're by and large Canarian so while Echeverias tolerate and and some even need hot, dry, conditions, most Aeoniums need milder conditions all year round.

How old were they?

Why do you assume it's an Echeveria?

It's an Aeonium.

I planted this Dioscorea in August 2018. 20190504_113929-530x771.jpg It quickly germinated and grew leaves. The leaves began to fall in March, so I thought it was entering summer dormancy. I stopped watering it. At some point in the past couple weeks, it has sprouted another leaf. Am I supposed to k...

Some of those are extremely common (Gymnocalycium mihanovichii), some are really common (Sulcorebutia), and some are not uncommon in specialist collections (Yavia). I have all three.

And some aren't even cactus!