You're modifying the document, so you may very well need some PDF specific software. Nothing special is needed to scan the document for a specific character string.
No - just searching for key words, and excerpting brief passages for my notes.
There is actually an Adobe pop-up that says I have to subscribe in order to search.
I presume it's some kind of lawyer thing.
I receive, or link to, other PDF files every month, including Adobe files from other sources, and they scan and excerpt just fine with Windows 10.