Many journals have a particular style for citations, but the style differs from one journal to another (or at least from one publisher to another). When authors are left free to select their own styles, even more variation results.
I've come to prefer a style in which (1) authors' names are given in full, including their first names if I can find them, (2) titles of articles or chapters are in roman type and enclosed in quotation marks, (3) titles of books and journals are in italics, (4) cities is which books are published are omitted. I'm not sure I've ever met anyone who agrees with me on all of these.
As for footnotes, most mathematics papers don't use them for pointers to the literature. They're used mainly for tangential additions to the main text, and they are fairly rare (except for acknowledgements of grant support). To refer to the literature, one would usually use a pointer in the main text; this can have many forms like [Blass and Sagan 1986] or [BS 1986] or [BlaSag 1986] or (my favorite) .