Is it good practice/advisable to sum up passages from a reference into a few sentences in my own paper?
I know people who restate whole proofs of mathematical theorems, either because the proof itself is interesting, or simply because the original presentation of the proof is poor in their opinion.

It is completely fine to summarize works of other people in your work, you just have to make it completely clear that it is not your work. But you can quote even whole paragraphs IMHO, without much problem (surely in math/natural science, I'm not sure how's it in philosophy and such).