Even "generic" succulents can be pretty;) 'Firestorm':) I wish I would have taken a picture earlier when this thing was blooming. It had white blooms everywhere:). The second pic is 'Opalina'. Third and fourth pic is just your plain old ice plant. When those things bloom I'm pretty sure even the most stuck up succulent person would be stopped in their tracks.

It is very small to correctly ID. Was it always so small? If not, do you have 'before' photo? In 4 mo, it should be quite a bit bigger. What I can tell you for sure, it needs to be repotted into much better substrate; in a clean pot (same one is most likely plenty enough in size but needs/should be washed thoroughly); pot should have drainage holes (I am assuming this one does); pot should be filled with mix much higher so plant is not lost inside of it (not helpful for few reasons); and it needs plenty of sun. If you are able and willing to make these changes - plant will grow and soon could be ID-ed. Btw, all improvements I pointed out would apply for growing almost all succulents, regardless proper names:)

If your soil has food or nutrients already, then you don't necessarily need to add more fertilizer (eg, Miracle Grow's Cactus Soil). You will usually see on the bag something like "feeds for 3 months" or "9 months" etc. That tells you there is already fertilizer there. That also means that is a guideline as to when you'll need to change out the soil. It doesn't necessarilly mean all the food has been taken up, since the roots may not yet extend to the entire pot, but use it as a guideline. So you could leave the soil longer if you wanted to. The other guideline can be that you'll want to repot about once a year...or when the roots are getting root-bound. As you can see, there are several ways to decide when to repot, and a lot of it has to do with how fast things grow or use up nutrients, etc Now as for specific food, some plants will benefit from other nutrients, too. (eg a plant that is about to flower, could use more than just what is in the plant food of the soil). That is why, even with plant food in the soil already, you may still want to supplement for the plant. In that case, follow the guidelines mentioned on the food package. But let's say the soil mix is something you created on your own, without the commercial plant foods already mixed in. Then you'll want to add your own regimen of fertilizers at the recommended doses.

The two leaves are goners. In the growing conditions shown, the plant will not survive. Does it even have roots, or is it just a cutting sitting in that purple stuff? I'm sure it was pretty before the two leaves started to fail, but succulents will never do well in such conditions. If you want it to grow and thrive, you can get a small pot with holes in the bottom (plastic or clay). You will need a bag of cactus and succulent mix and a bag of perlite (or pumice) from your nursery. Mix them together 50/50. When you repot, get all the potting mix/purple stuff off the roots, then repot in your plant in new proper mix and don't water for a day or two. When you water, let the water run out the bottom holes, then don't water again until the plant is dry. No "sips" of water. Gradually transition your plant into the brightest light you have. I hope you don't mind all the instructions, but plants sold this way don't last long. It needs help!