If not, can APK files for Android run on either ARM CPUs or non-ARM CPUs?
Sorry for my poor English.
Android runs on other CPU's as well. Such as Intel Atom.
If your app uses only Java then it doesn't matter. It can run on any CPU and you won't care. You don't have to program specifically per CPU when working with Java.
If your app uses native code (NDK), then you'll have to prepare your APK to run on all CPU's you want to support. Instructions such as these explain how to do so.
If you're not sure if you need NDK or not, then you probably don't. NDK is needed in very specific cases such as high performance games. If you're just making a regular app, you will probably use Java only.
Regarding the APK issue - if you need to support multiple architectures you can do this using both a single APK or multiple APK's. Read this for more info.