[AUCTeX] autocompletion for \newcommand and LaTeX-math-list simple example

[Renato]

Hello, I'm very new to auctex and wasn't able to find an answer to
these, so I'm asking for help here.

1) I have some \newcommand in the preamble of my file; is it possible
to have them appear as suggestions in the autocompletion (C-c RET) list?

2) I have several particular symbols I'll be using a lot in math
environment, and I'd like to have them as shortcuts in the math mode. I
read how to customize LaTeX-math-list , however I'm at a loss as to
what the second argument ("a string representing the name of the
macro") should be. Could someone give a me simple example for how to
bind ` f to \iff ? That BTW would include overriding the
default ` f which is \phi 

best wishes,
renato