What should I do about my cacti? I'm a new plant-owner and I thought that they were growing fine at first but now I'm not sure what to make of it. Do I let them grow as is, or should I cut them? And if I do cut them, can they be replanted on their own?
Strange Cactus Growth
They look great! You are seeing it growing new 'pads.' You have an Opuntia there. Google 'opuntia' so you can see what it is growing up to be which is huge. Yes, the pads can be taken and will root on their own. Generally you let the cut part heal over for a week or so before you plant them. Look on You Tube for I am sure there are videos showing you how which is so easy.
Your pads are immature. I am not a cactus much less an opuntia expert. There are tons of them. I wonder if yours are Opuntia ficus-indica, a very common one.
Opuntia ficus-indica, at the Ruth Bancroft Garden. Picture from internet.