Yes, we should seek to understand it. Even if we may never have a full answer.
No, there are better uses of our time.
It can help us make predictions on the future of the universe.
It is absolutely vital to seek to understand all things around us. Are there more pressing matters demanding our time? Yes. However, it is still not a question so irrelevant that it should be abandoned.
I would say understanding, or at least attempting to understand how the Universe came into existence would open doors to other mysteries. Such as dark matter etc.
Gives us the will to figure out problems. if we try to tackle the biggest problem, it might help us solve other problems.
The theory of eternal inflation is an active field of research in theoretical cosmology which has recently been tested empirically with the BICEP2 and Planck instruments. According to the theory our local universe did have a beginning. This is an indisputable scientific fact with a little less than 100 years of data to back it up. However, whether the entire multiverse, within which our universe exists, had a beginning is a different question. Work by Alexander Vilenkin has shown that this multiverse cannot be eternal temporally towards the past. As such the multiverse must have had a beginning. Furthermore, this theory of inflation is not pseudoscience as it makes detectable predictions in our universe. Thus, this question is indubitably within the realm of science.
Yes and no. I think we place too much importance on it instead of simply loving each other and dehumanizing each other.