changing the color of an imported PDF

The suggested preflight routes are good. and if you happen to have Pitstop (likely not. 'cause it's pricey), even better as it has amazing control over changing items in PDF files more so than Acrobat itself..

That being said, there's no harm in trying the Illustrator route when you don't have access to an original file. Who knows, the file might have originated there anyway and might be a PDF saved with Illustrator editing preserved, in which case you might just face some missing font issues. (If you check your PDF's document properties, it usually states what the originating program is)

Even if not, you can totally open any PDF file in Illlustrator. The biggest issue (among several) you will face, again, is fonts. You need the fonts yourself to edit the file, and since PDFs are usually saved with font subsets (with new encoding), there's a good chance your file will open as text gibberish even if you do have the correct fonts.

Besides fonts, if the PDF had images and transparency effect (especially if flattened), you will see the illustrator file is now broken up into several "tiles" and other artifacts. If this is the case, best to abandon this approach.

Again, it depends on the file!

You can change a specific color in a pdf using an Acrobat preflight, here is a link to a related discussion:

https://community.adobe.com/t5/acrobat-discussions/how-to-convert-all-text-in-a-book-from-cmyk-to-black-only/m-p/13286263#M383961

You can also probably do this in Illustrator (as mentioned), but be aware that Illustrator is not a universal pdf editor and you may see unexpected changes, particularly in pdfs that were not created in Illustrator.

Best bet is to go to the original source files, edit there, and re-export. If you don't have that, the PDF would need to be edited by either Acrobat or Illustrator, but you need to be careful nothing else gets messed up by doing so. PDF format is not meant to be edited, so it can be a bit finicky. 

I'd avoid Photoshop so it doesn't rasterize the PDF if possible, assuming you're talking about vector content.

Try to edit it in Illustrator - depends on the contents it may not be so hard.

There are tools for Acrobat Pro to do that. I do not recommend to openen the file in Illustrator or Photoshop as it will cause other sever Problems, but this is often done.