How can I get Emacs to reload all my definitions that I have updated in .emacs without restarting Emacs?
You can use the command load-file (M-x load-file, and then press Return twice to accept the default filename, which is the current file being edited).
You can also just move the point to the end of any sexp and press C-x, C-e to execute just that sexp. Usually it's not necessary to reload the whole file if you're just changing a line or two.