I am trying to test my app and I have lots of problems with Android emulators. Finally, I got one emulator running using Android 2.2 . So I used this one and my app works fine.
I also tested my app using real device, Nexus 7 , Android OS 4.2. App works fine in both versions.
It is safe to consider my app will run fine for OS versions within 4.2 - and 2.2 band? The reason I am asking is because using emulator makes my computer very slow and it takes forever.
In the best case: yes. In worst case: no. It completely depends on the parts of the Android API you're using in your app. For example, private APIs might very well break or change. You should be fine with public APIs, but there's always the chance of a bug in one of the OS versions...
If you want to test your app on various devices and Android versions, you should give apkudo.com and testdroid.com a try.