No, but it's complicated. You can fork the android source which is under the Apache 2 license: http://source.android.com/source/licenses.html

If you want to use the Android SDK (this includes additionally Google APIs), you have to agree to this license: http://developer.android.com/sdk/terms.html This is also needed to release your App in the Play store.

Someone has argued source.android.com should be given a different name, similar to chromium and chrome. I think that would clear things up, too.

Not at all. This isn't about forking Android.

People who fork Android wouldn't really benefit from offering a separate SDK anyway. They would want to take advantage of the existing app ecosystem and preserve compatibility, just like Amazon is doing with Kindle Fire.

A fork means that you offer an incompatible SDK. What Amazon does is not forking the SDK, but using it.