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On the Home screen, there should be a 'Settings' button.
To the left, scroll down until you find the 'Skype' bar
And there, should be a button that says 'Go Offline' and you can choose the amount of time it takes until you go offline while Skype is running in the background.
I use an iPad, but the iPhone should be similar. Hope I helped!
Do you think I could reduce the size of the pictures? They are about one-inch square - very uncomfortable, The PC version and the iPhone both have small icons. That would be a help.
I'm not sure this is the answer you're looking for, but, as far as I know, the iPad itself is sort of designed that way. Well, it's more the fault of the OS, technically.
Most things/Apps on iPads look zoomed/magnified when compared to iPhones.
I'm not surprised Skype is the same way.