Your tale about 'apps' is revisionist history. It's simply not the case that apps was a commonly used synonym for 'computer programs' until after Apple popularized its use on iOS. And, most usage before that was restricted to Apple/NeXT platforms, which used .app as the extension for application bundles. Prior to usage with iOS, while 'application' was used, 'program' was much more common, and even 'executable' was still more commonly used than 'app'.
As for your second point, think one word: Windows.
The phase "killer app" has existed for almost as long as personal computers themselves. Wikipedia says that its origins are with VisiCalc on the Apple II, way back in 1983.
I don't know a great deal about US IP law but English IP law is very clear - you can't trademark generic terms related to your business. If you sell apples, you can't trademark apple. If your business is in Ohio, you can't trademark Ohia. If your name is John Smith, you can't trademark John Smith. Both of the term "app" and "store" are generic when related to selling applications from a virtual store.
Actually Apple has always use the word Applications for executable on classic MacOS platform where Microsoft has always used Programs (fun fact: MacOS has always used APPL has signature for executable) . While Visical pre-dated the MacOS, the terms Killer Apps was coined long after it.
Edited by BigMac2 - 9/27/12 at 12:07pm