You appear to have a healthy Echevaria succulent, not a cactus. Leave the buds to grow and form a clump, or you can remove them when they have formed their own roots to start another plant. Old leaves shrivel and dry up as yours appear to have done, not rotted. Gently pull them off to improve the appearance of the plant. Your pot is far too large for the size of the plant.

As sg said, the pot is way too big. It needs a very small pot with drainage holes. It will not do well in that pot. Plastic is fine but I prefer terra-cotta. The pot could be just slightly larger than the width of the top of the plant, as a guide.

You can repot in a fast draining mix. Most frequently recommended here is commercial cactus and succulent mix combined 50/50 with perlite or pumice available from nurseries. If perlite, rinse tiny bits out through a strainer first. Get pumice if Available.

just leave the long sprouts for now. They could develop into new plants for you as they grow larger. Oh be sure the plant gets plenty of light but probably not all day sun.

Thanks for the advice guys!!! Really appreciate it!!!

Corrected the above to say the pot can be just slightly larger than the width of the plant.