I wash fabric before cutting. I usually do NOT iron it until right before I'm going to cut it. No sense in doing it twice.
Some of the selvages shrink drastically during the washing and drying process. I will clip those selvages at about two inch intervals so that they will lay flat when I iron/press the piece.
As far as determining the 'width' of the fabric versus the 'length' of the fabric:
Usually, woven fabric has more stretch across the width (crosswise grain) than along the lengthwise grain.