The word "take" is more connected with the word "serious," as in the phrase "to take something seriously." It means you regard it seriously or you are genuine in your concern; you are not casual or disinterested in it. You could say: Mr. Obama gave his first Oval Office speech on the problem to show he took it seriously. Mr. Obama gave his first Oval Office speech on the problem to show he was serious about it.

not really... maybe it could mean to "manage" the problem. " we're going to take a problem and iteratively develop the solution..." but if you say. "to take a problem away from someone", it means "to relieve somebody of something." :)

Not so obvious. Can you add more to the question?