Pressing the menu button brings you directly to the desktop, but leaves the app running. Pressing the back button to get out stops the app.
Getting to a download depends on how you're downloading - some browsers have addons that allow you to manage the downloads (and that changes daily - people are always writing new addons, and updates keep breaking old ones), Play allows you to run an app as soon as it downloads and installs, but you usually have to go through a file manager or Downloads in the app drawer.