You will need to search through photos to identify your plants. Here are ONE and TWO for cactus, and here is one for SUCCULENTS.

Those grafted cactus with yellow and red color (and maybe the one in the third photo from the top) are clones that lack chlorophyll and can only survive due to their graft to the lower green cactus. Although the green cactus is tolerant of both over and under watering, the colorful tops usually live only a few years. These have common names of neon or moon cactus. These should have bright light but not sun or they will sunburn. HERE is an article that gives more detail.

Stefan, I provided two links for cactus identification and a third for succulents only. I never referred to all of her plants as succulents. However, the link I supplied for succulents opened in the middle of the page on Cactaceae instead of at the top of the page. I have corrected that.

YOur tiny leaved purplish sedum could be s. oreganum.

The green echeveria in the 4th photo is an echeveria elegans mexican snowball.

agreed with mexican snowball, as the 4th green one.