Use this handy tool called the "V-Cam" to solve all three of your problems.

In the bottom layer of the animation, draw a big background encompassing the entire area that your animation will take place in, even if it spills over the boundaries of the stage (the area that appears in the exported swf, designated by default as the white area).

In another layer, place the V-Cam movie clip. If it is a different size from your file's stage dimensions, simply click the movie clip and in the properties window (show at the bottom here) you can set the Width and Height to match your stage. From this point onwards, Flash will treat the stage as the area within the V-Cam instead of the original white area, so by animating the V-Cam to follow your action, the .swf will always follow it accordingly.

Also, the V-Cam can be manipulated to produce effects like screen-shaking (simply animating the camera jittering around).