Extract the x/y part from a coordinate in pgfplots

I'm not aware of any direct syntax to do that (though I would love to have one). You can however use the let operation (section 14.15 in the TikZ v2.10 manual):

\usetikzlibrary{calc}

[...]

\draw let \p1 = (A) in (\x1,3) -- (0,0); 

For the second part of your question: You can do that with the |- syntax.

\coordinate (A) at (1,2);

\draw (A |- 0,3) -- (0,0);

Note that for pgfplots you need to set the version to at least 1.11 (e.g., \pgfplotsset{compat=1.11} or \pgfplotsset{compat=newest}) or use coordinates in the (axis cs:x,y) format for the intended behaviour.