changing css in a template

Yes, we need to see the code.

Also, what's this supposed to look like on handheld devices (mobile & tablet) where there's less available real estate?

You will have to share the code for us to offer advice on what you could potentially do to remedy your situation. But based on your feedback thus far, moving the logo that far on the page would not be only a CSS move, but rather a move in the HTML as well as styling for the area you are trying to move it to. 

For the moving of the body content, by moving the content left it will likely throw the page out of balance as you likely have a container with a defined width centered on the page. So if you move content left of that center, you are either thinking about widening the entire body content width of your page, or unbalancing your page by stretching your content into negative space. Something to consider in this instance is looking at your page in alternate screen resolutions and you might find that while on a higher resolution monitor like you may there may be extra space in the gutter, on a smaller screen that content may touch the edge and moving into the negative space could cause that content to be not viewable without scrolling.