Sometimes -- it depends on what you are doing. If you are commenting on the original, you often can qualify for "fair use" -- which allows you to use copyrighted work without asking if you are commenting and if you take only a modest amount and in a way that does not much harm the original copyight holder.
As for permission, I think it would be very hard for a normal blogger to get the attention of a major magazine to get permission like this. You could try (email customer service) but my guess is that you will not get a response.
Overall, be sure to be modest. If you take a giant version, or take every cover every week, you will get in trouble. But small-scale copying in the context discussed should typically be okay as fair use.
The fact that you are making money does not much alter the analysis. A professional book reviewer makes money, but he still can quote the book (modestly) and rely on fair use to protect him. So that's not a big issue.
Screen shots would again have to come under fair use, where you need to make sure you are taking only modestly, not causing economic harm, and so on. But a conventional press page is likely not to cause any problems.
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