I guess that the answer to 3 is the following. The tradition in math is to write the names of authors by alphabetical order. But then the number of collaborations has been increasing, and the contribution of different authors is not always well-balanced. Such appendices are, in my opinion, a way to keep the tradition and adapt it to the new situation (more and more collaborations, with sometimes contributions being somehow significantly different).
About question 1 let me consider an example. It is a paper by Galyna Dobrovolska, John Kim and Xiaoguang Ma, where the authors study the lower central series of an associative algebra, regarded as a Lie algebra. At some point they need a general result, which was proven by Feigin and Shoikhet in the particular case of a free algebra. I guess that Pavel Etingof told them that he knew how to prove this result, but probably did not want to write an independant paper about it. On the other hand it might be that this contribution is not as significant as the work of the main authors. So he wrote an appendix to the paper.
Now about question 2, if we still consider the same example, here is how I would quote the paper (according to mathscinet):
[DKM] G. Dobrovolska, J. Kim, X. Ma, On the lower central series of an associative algebra (with an appendix by Pavel Etingof), J. Algebra 320 (2008), no. 1, 213–237.
Concerning list of publication, if you write an appendix to a paper it probably means that you don't need/want to increase the number of your publications. But anyway, for the list of publication you can write something like this
Appendix to the paper On the lower central series of an associative algebra by G. Dobrovolska, J. Kim and X. Ma (J. Algebra 320 (2008), no. 1, 213–237).
