Is there a way to copy apps from one iPhone to another one that has no service?
I think if you bought the app (you have it in iTunes), then you could copy it to another Apple device that you own that supports the app - but by syncing the device via iTunes. But I've never copied an app to another device (my iPod is much older than my iPhone and doesn't support apps).
If the device you are syncing to isn't paired with the computer where you're running iTunes, then you'd have to blow away everything on the device that you want to sync - then it will sync with your iTunes library. I had to do this once when my iPhone got bricked.
I'd advise you to take a look on Apple's iPhone forum for more information about downloading your apps to more than one Apple device (such as an iPod Touch, iPhone, or iPad).