ArcMap window size

I need to draw on the ArcMap window - but I have two questions:

(1) How to know the size in pixels of the ArcMap window? I need to know the size of the area where ArcMap renders the map.
(2) I also need to know how to transform coordinates to and from the local (i.e. screen coordinates of the ArcMap) and Map coordinates.

Will appreciate any help on the above!