It means something like, "Well, I suppose that the rain is useful," or "I suppose it's always beneficial for the rain to fall." It's the kind of thing someone would say if it's been raining and they don't really like the rainy weather, but they realise that it has benefits (it helps plants to grow, it cools the temperatures, it provides us with water, etc.). It is different from "We can *really* use the rain." This conveys that the rainy weather is very welcome; perhaps it has been extremely hot and dry lately, so the speaker is really happy that it's finally raining.

Yes, in that context it would mean it's been raining recently. To me, it also sounds like the speaker isn't that happy that it's been raining, but is acknowledging that it's at least good in some ways.

Thank you very much. :)

I agree with Vaughan that it's all about the context. Asking "How about this weather, huh?" could indicate that the person asking the question is implying that the weather is not good. The person replying "I guess we could always use the rain" could be affirming that sentiment, agreeing that the weather is not good, but also suggesting that there is an upside to the rain. For instance, perhaps their location is in a light drought and in need of rain for the crops.