Good luck. Root beer is like pickle juice - damn hard to eradicate. That's why most poeple that serve root beer do it in a dedicated keg on a dedicated serving line & tap.
Yes. But most of our used kegs have held syrups before and some of them had to have held root beer.
I would give it a long soak with oxyclean and a detergent. Start with hot water. Disassemble everything and soak the posts and dip tubes. Throw out the rubber. After soaking, scrub everything with something like a clean toilet brush. I would use a diptube brush, too.
Leave it open to dry out. I've found that sealing the kegs before they dry can help capture some of the lingering odors. Leave it open for a while. Smell it and repeat as needed.