I generally like writing custom commands, here's the one for your first replacement:
(defun replace-plus-minus ()
(interactive)
(replace-string "±" "\pm" nil (point-min) (point-max)))
But, you can also use keyboard macros. Check out the wiki and docs.
Basically, you'd do:
C-x ( M-x replace-string ± RET pm RET C-x )
Then you can name it, and save it to your .emacs:
M-x name-last-kbd-macro
M-x insert-kbd-macro
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