Do I need "Introduction" and "Conclusions" parts in my PhD thesis?
Run, don't walk, towards the advice of your advisor.

I'm not sure why you are questioning their "experience writing a thesis in parts."

You should add a broad introduction and broad conclusion that service your entire thesis; these will be before and after your Part 1 and Part 3, respectively.

You should add individual introductions and conclusions to each Part. Therefore you will have a total of 4 introductions and 4 conclusions, with 3 of each that have a narrower scope and 1 of each that have a broad scope.

You will probably additionally have introductions and conclusions within each chapter in each part, though you may not label them as such and they could simply be paragraphs. This is simply good writing and is not at all related to thesis writing specifically.