"Where are the first-authored papers? In what field do we see them most commonly?"
I think, in Mathematics and Theor.Physics, and in general in any Theoretical Science.
" Why is it becoming increasingly rare to see single-authored journal papers?"
I think, unfortunately, the reason is very often not from research, but from finance.
Researchers report by their publications: the more publications they have, the better.
When I was a student, professor in Nuclear Physics gave us to solve 400 tasks/problems for two weeks. How do the students from our group? We spread the problems between all students (who have been able to solve them), say 40 problems to one student, and then exchanged by solutions. In the modern "research world" the situation is very similar.
What has negative effect for science, as a whole.
In ideal, your salary should not be connected with number of your publications, and should be as more "socialistic" as possible. The ground (for administrators of funds and grants) that they support the most talented on the basis of a competition is an absurd, if to remember how worked Newton, Euler, Gauss, Maxwell, Mendeleev, etc. They would never be able to obtain a grant, because they would never be able to write a good report, as I afraid.