I have a lot of Word & Excel documents. I used to have office for Mac until it failed with an upgrade a couple of years ago, then I subscribed to Office, but I'm tired of the $99 per year. My wife doesn't need Office at all, if I can copy the documents she needs into Pages. I need it for some sharing and at least one spreadsheet with macros. So I'm not familiar with Pages & Numbers. Apparently, I needed to convert a bunch of fonts to themselves (ariel to ariel) by selecting them in the drop down menu. Ugh what a pain. And the two fonts that it didn't find converted to other stuff. That got rid of the problem for this document. But I have to do that for every document I want to convert!!!
I can’t speak for Pages at all since I consider it one of the “junk” Apple apps, alongside Books, Music, among others.
Try one of the free office suites in place of Office. My favorite is Libre Office. It might give you better control over the Word document than Pages. Next time you get a Word document, it will help if you can ask for an accompanying PDF file. PDF files, if properly generated, will embed the fonts used in the source application. That’s what the P in PDF stands for, portable. It will, at the very least, show you what the Word file was intended to look like.
By the way, what is the final format that you wish to get? Pages documents are terribly difficult to convert to other formats, so unless you plan to be a Pages ace, I would suggest settling on another program or suite to manage your documents.