At my institution, I am required to publish four papers in addition to my PhD thesis. Of course my planned papers are related to my dissertation project, but I'm not sure if it could be considered academic dishonesty / plagiarism to use these works to form part of my dissertation. I'm not thinking about copying them word for word, but I was hoping that I can include summarized versions of those works as chapters in my dissertation. Is this a common practice or would this be considered self-plagiarism? Should my dissertation work be completely separate from those other publications?
Depends probably on the rules at your institution. At many places actually this is the usual custom. Ask your adviser.
If you write out the correct references so that everybody who reads knows that this part can be found in that paper, then it is never plagiarism. See also the "Sandwich thesis" question mentioned in the comment by Andy W.