Is it possible to run Emacs.app with ~/.emacs.d/init.el and Emacs2.app with another init.el file that's placed somewhere else? If so, how?
Yes. Inside the Emacs.app folder is an executable that you can run directly, with some command line flags:
/Applications/Emacs.app/Contents/MacOS/Emacs --no-init-file --load /my/other/init2.el
(Your Emacs.app may be in a different folder)