You can play blues on whatever you want. A slide is used in that song. You need to know the blues scale, standard blues progressions, and you might need to learn a few alternate tunings since Robert there has a tendency to be tuned funny at times.
Well, you can use a slide, but not all blues uses that. Pick up an album or two, something like Buddy Guy, Chuck Berry, T-Bone Walker, BB King.. They're all great records to get the feel of the blues in my opinion.

Then, as the guy above said, learn the blues scale. It's on all-guitar-chords.com as virtually every other scale is, I think.

The great thing about the blues, is that anyone can play it, and you don't need to be lightning fast across the fret board for it to sound great!
If you want to emulate the original Delta blues styles, Johnson is a good start. Also guys like Skip James, James Elmore, Son House, etc, etc. Just pull up a few of these guys on YouTube and then start playing all the cats that are linked to them.
Much (not all) of this is indeed slide playing in open tunings. "G" "D", and "E" being the most popular.
Again, there is a ton of instructional material available. Slide masters like Bob Brozman and Roy Rogers have DVDs available and also a lot of material on YouTube.
If you're starting from scratch, I would suggest doing a lot of listening to all those guys. You're looking at the roots of rock & roll there.
Well....Likely not. The nylon strings are too slick to provide much tone. However, to start with, even a cheap pawn-shop acoustic will be fine. In fact, on Brozman's DVD, he suggests buying a cheap acoustic to start out with as you should set it up with a high action anyway, and it'll be in open tunings most of the time.
I bought a seriously-cheap guitar and converted it into a resonator.