Root Loci Breakaway points
Breakaway points signify the points where the loci of poles of a system meet and branch away from the real axis and into complex space to terminate at open-loop zeros in the plot, or those at infinity. There are also break-in points where the loci of complex poles rejoin the real axis and approach zeros.

When sketching a root locus plot, valid regions of the plot that lie on the real axis are the regions to the left of an odd number of poles and zeros. When such a region exists between 2 poles, such that their loci have no where else to go but towards each other, it is guaranteed that both loci will meet at some point (determined by the roots of dK/ds) in that region and break away from the real axis to approach either some explicit zero or an implicit zero at infinity along known asymptotes.

Trying to answer your questions:


There are no breakaway points between zeros; you may have break-in points though, as the loci of other poles terminate at these zeros. 
There is no guarantee that a breakaway point will occur exactly halfway between 2 poles; the position of the zeros (if any) influence this. 
If the portion of the real axis between the pole at -1 and the zero at -2 is part of the locus, as determined by the rule I mentioned earlier, then yes the pole will travel towards the nearest zero and there will be no breakaway points between them; in fact there can be no breakaway points between a pole and a zero.
You may have a double pole (e.g. s = -2 twice) and the loci of both poles will break away from their very beginning at s = -2. You may also have complex 'breakaway' points, where 2 loci meet in complex space and diverge. I dont know of any other.