For your first, question, you're going to want to use the clipping functions available in the Data Frame Properties, all the way down the page on the resource center link. Go to View > Data Frame Properties > Data Frame > Clipping Options and set the clipping options to the data driven pages extent. Then, if you'd like to exclude any layers from the clip, (for example you had imagery in your map and you wanted to display it beyond the boundaries of the index polygon while clipping everything else, you'd exclude the layer from the clip). Set the border to a line to distinguish the polygon. Can you upload a shapefile of your grid features?