A: Depends on what kind of shelf you're trying to build. Furring strips aren't usually that straight or dimensionally consistent, because they are... well... just furring strips. They also don't have nice 90 degree edges. If you're looking for more of a "finished" look, you should consider pine or poplar.
A: Not a staple gun, bit you can use a smaller Guage finish nail that should hold it in place just as well
A: They are 3/4 inch thick so probably not.
A: Yes, these absolutely can be stained. I make frames out of them and it takes stain well
A: Yes, but you have to leave the stain site for a while
A: If you have seen them first...they are not finish grade, very rough, but yes, it would absorb a stain.