Hi @dstewart_gb,
Allow me to try and answer your queries in order 
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It sounds like you’re hitting up against a known bug in the media server re. poor randomness. The issue has been identified, and a fix should be arriving soon! Beyond that, the algorithm for this favors highly rated tracks (star ratings), popular tracks (based on last.fm metadata), and tracks that you’ve not played recently.
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This is entirely dependent on the server, and it sounds like your music might not be properly tagged or matched. Styles are brought in from AllMusic, so if you’re missing them, it’s likely one of several things. Firstly, make sure you’ve upgraded to the new Metadata Agent. See here: https://support.plex.tv/articles/upgrade-music-libraries-new-metadata-system/. Are you using the “prefer embedded tags” setting? If you’ve enabled that, you need to manually make sure your music has the appropriate tags. I’d probably suggest disabling that.
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Outside of the randomness issue, what other bugs have you found in radio? I’d love to be able to get these reported to the devs for you! Have you tried Mix Builder? It might give you some of what you’re after (effectively multi-artist shuffle). As a workaround for multi-genre shuffle, you can create some smart playlists for the genres you want. There’s a great user guide in the forums that might help you out with this:
From the sounds of it, your main problems seem to be to do with the way your music library is set up. Let me know if you have any more questions, or if I can help you get things running a bit more smoothly!
