The cactus might be an echinopsis. Does it have big, showy flowers? The brown part is probably corking after some old damage (sunburn? frost? mites?). As long as it is not spreading quickly it shouldn't be a problem. The last one is definitely an Aloe, but probably not A. vera. I don't know which one, though. These could all use more light. If you are moving them into full sun, be careful to do it gradually so they don't sunburn.

All houseplants plants need drainage, at least one hole. The pot is also too big for the plant as I suspect the roots don't fill the pot entirely will a little free space for growth? Media is the soil mix its grown in when used in this context. Your 'soil' appears to be dark and fibrous which to us indicates a high peat content. Aloes, like most c/s plants need sharp drainage, so one with lots of grit or perlite. You need to add as a minimum 50% of something to a c/s mix to get that, for e.g. perlite, pumice, small horticultural grit or aquarium gravel, or search in the box at the top for a suitable gritty mix. Inspect all the roots for hollow, squishy, smelly bits and the collar of the plant where the leaves grow from, there could be a brown portion that I'm seeing, is that soft? Seems like the remains of another rotted leaf there? The leaf appears to have rotted and is done for probably because of the problem with your soil. Despite infrequent watering, this kind of soil can stay wet for ages if it's not being dried out by the plants uptake of water.

Looks like it is quite lacking sunlight. That is probably what is making it so floppy... Hard to ID right now, as it is not in the best shape, but I could hazard a guess at Haworthia maybe? Anyways, it looks like it needs a repot. Get a smaller pot for it. For soil, use some perlite (sift it) and cactus and succulent soil, mixed about 60% perlite 40% soil.

They seem to do that when too dry, they loose the gel in the leaves and fold in. As said above, make sure to have it in a pot with good drainage. Since it's the older leaves I wouldn't worry too much. Just leave it alone until the leaf turns all crispy brown then can be removed.