I would like to know please whether or not I can pick up alien radio signals from my backyard.
This is like asking "can I spot polar bears from my back garden?"
There is nothing that would stop a determined polar bear from coming into my garden, so it is not impossible. But unless you live in Churchill, its probably not going to happen.
You can get a radio telescope, and it would be able to receive a sufficiently powerful signal. But detecting alien signals is hard: so far we haven't detected any. Even with big detectors.
Can you detect aliens: Yes. Will you detect aliens: Probably not.