Q5 - Ask Amazon.
For what it is worth, Amazon doesn't manage to support periodical format on KF8/azw3 so it's rather unlikely to support periodical format on an epub to mobi conversion since epub does not support the rather proprierary periodical format (AFAIR, azw is mobi with Amazon's DRM).
Since you are using your computer to download the news, just connect your Kindle and transfer the .mobi files if you want to use periodical format mobi files. Since you only mention a single device you are using for reading, I can't see it as being that much of a hardship.
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