4) 2 & 3
Extending the Binder class
If your service is private to your own application and runs in the same process as the client (which is common), you should create your interface by extending the Binder class and returning an instance of it from onBind(). The client receives the Binder and can use it to directly access public methods available in either the Binder implementation or the Service.
This is the preferred technique when your service is merely a background worker for your own application. The only reason you would not create your interface this way is because your service is used by other applications or across separate processes.

Using a Messenger
If you need your interface to work across different processes, you can create an interface for the service with a Messenger. In this manner, the service defines a Handler that responds to different types of Message objects. This Handler is the basis for a Messenger that can then share an IBinder with the client, allowing the client to send commands to the service using Message objects. Additionally, the client can define a Messenger of its own, so the service can send messages back.
This is the simplest way to perform interprocess communication (IPC), because the Messenger queues all requests into a single thread so that you don't have to design your service to be thread-safe.

Using AIDL
Android Interface Definition Language (AIDL) decomposes objects into primitives that the operating system can understand and marshals them across processes to perform IPC. The previous technique, using a Messenger, is actually based on AIDL as its underlying structure. As mentioned above, the Messenger creates a queue of all the client requests in a single thread, so the service receives requests one at a time. If, however, you want your service to handle multiple requests simultaneously, then you can use AIDL directly. In this case, your service must be thread-safe and capable of multi-threading.
To use AIDL directly, you must create an .aidl file that defines the programming interface. The Android SDK tools use this file to generate an abstract class that implements the interface and handles IPC, which you can then extend within your service.