No, the verb "to rain" does not express finished action. The continuous tenses are continuous because there is no clear end point in time. What grammar rule are you referring to? It had been raining since morning when we went out, which is why we brought our umbrellas with us.

No. It sounds like it was still raining when you went out.

Are you trying to say you went out in the morning, or at some point later in the day? The sentence could be interpreted either way. Also, "since" does not imply and end time. Both actions occurred in the past, so it seems to imply that it was still raining when you went out.

it seems to me no. the continious form of the verb "raining" means that the action is not completed yet