I agree with Alex. I would add that “resolution” often suggests a certain amount of subjectivity: there is a human decision about what to do; there may have been many possible options; it is not necessarily clear what the best option is; but somebody made a decision to choose one of the options. In contrast, “solution” suggests more objectivity: there is a problem, and the solution provides a clear and effective way to overcome the problem.

Sometimes they are interchangeable but "resolve" also often means to make a decision, and in this form does not take an object. Sentence #2 is not colloquial and doesn't quite sound right. The other sentences are fine, but 4 would be much more common than 3.