Under Theme Options > Sidebars click “Edit Sidebar” on the one you want to add the background to, scroll to the section “Sidebar Background” and click the “Choose Image” button. Upload your image, click “Use Image” and then click on “Save Settings”. Your image should appear as a parallax background on that sidebar now.
You can move and reorder widgets anywhere on the page and they will maintain their styling everywhere except the “Full Screen Header” sidebar. That’s a special case sidebar designed to fit content above the fold, as it’s documented here.