I first tried to make an object box on one side, and was trying to figure out how to mirror it to the other side of the page. But I don't think that's going to work.
Draw two boxes. InDesign doesn't “do” live mirror effects (such as Illustrator does). Use the ruler and the control panel at the top plus some math to position them on the exact mirrored location.
What I'm going to try right now is to just draw a box the entire width of the page and use a swatch to color it grey. Then try to put another object on top of it the width of the content box that I want to create, and make that one white. Is that the best way to do this? I'm worried that it's going to increase my file size greatly.
Sure, that's another way. A box is simply four coordinates and a fill color, so it won't increase your PDF file size by much.
My second question is once I get this done (however I get it done) how do I apply it to all the pages in my document? Do I have to manually create it on all the pages?
That's what Master Pages are for.