Android Developer Documentation: download?

You can get it under $ANDROID_SDK/docs/. If it is not already there download it via the "Documentation for Android SDK" option.

Alternatively you can download the source tree and link it up with your IDE.

Yes you can.

Open SDK Manager (located in android_sdk_dir/SDK Manager.exe).

In the latest API (4.2) select Documentation for Android SDK.

Once downloaded, you can find the documentation in android_sdk_dir/docs.

Can I download the entire Android Developer documents to my machine and browse it locally?

In the SDK Manager simply select "Documentation for Android SDK" for a recent API.