You should have a base copy of your resume in Word (or other such app). You can make edits and do "save as" for each version you need. Then you can make a PDF of whichever one you want to send.
Converting from PDF to Word is possible but it will mess up formatting, most likely. I'd start from scratch in Word.
Technically they aren't. You use a native app and then save or export a PDF. In this case Word, but other apps (as was mentioned) can be used.
To edit a PDF you need either Acrobat Standard or Pro on a Mac or PC. Even then, depending on the complexity of the PDF the standard editing tools don't always do the job. That's where plugins like Enfocus Pitstop Pro come in. If you've got about $800-900 to drop on a plugin.
I don't think there's anything equivalent on iOS to make the kind of edits you can on a computer using Acro Standard or Pro.
Reader definitely doesn't cut it for anything except reading.