Opening a DMG file and switching to it automatically
Not all .dmg files open immediately to show their content in Finder [I think it depends entirely on whether they were open or not at creation/last Save], so if they don't, you need to have your Finder prefs set to show External disks. This will then show them to the right side of your desktop, below existing mounted partitions.
That way, if they don't auto-show, you can at least simply double-click them to open.