I learned a lot from reading Bestvina and Feighn's article [Notes on Sela's work: Limit groups and Makanin-Razborov diagrams][1].  It's not a broad introduction to elementary theory, but it does express some of Sela's ideas quite succinctly.  You may need a background in geometric group theory (specifically, in understanding laminations on 2-complexes or group actions on $\mathbb{R}$-trees) to get the most out of it.

Regarding the question of whether or not the Hopf property is elementary: the answer is obviously `no' if you allow infinitely generated examples.  Indeed, consider the free group on countably many generators, $F_\infty$.  The elementary theory is completely determined by the set of finitely generated subgroups, so $F_\infty$ is elementary equivalent to $F_2$.  But $F_2$ is Hopfian and $F_\infty$ is not.

I don't know a finitely generated example, although I agree that one must surely exist.

  [1]: http://arxiv.org/abs/0809.0467