3-if you select and object , and hold shift -drag it to any direction it will snap to the direction you have moved it to (no need to select the desired axis then move it ) , this is helpful when you have long object , and the axis out of the camera view .
4-hold shift + moving an axis (this time you move the handles ) will move the object in the other 2 directions , e.g.
you shift click the X axis , the other axises (Y,Z) will be highlighted and if you move it (while holding shift) it will move in the Y,Z.