Help me save these succulents

I bought these a few years ago and they were all much smaller and potted together. One of them almost died when the stem became rotten but I trimmed it away when I repotted them all and it took and thrived. Now they are huge and leaning over.

My questions:

What type of succulent are these? Can I trim them without hurting them? What should I do with the small growths on the top right one?

They seem to be growing in such a way that there’s a whole new succulent forming on each one.

Thanks in advance!