What train from Fukuoka to Matsue?

Is there a scenic daytime train that goes along the coast to Matsue? How long does it take?

You could travel along the coastal JR Sanin Line between Shimonoseki and Matsue. There is no direct train. You would have to transfer several times along the way. Connections are extremely infrequent along some sections, especially between Nagatoshi and Masuda. From Masuda eastwards there are a few direct limited express trains.

So, a practical route would be via the Yamaguchi Line through the interior to Masuda and by limited express along the coast from there.

Thanks for your advice. I think I should plan to take the fastest train from Fukuoka to Yamaguchi, and then take the train through the mountains to Masuda and then Matsue. Do I need to change trains between Yamaguchi and Matsue?

This is a great tool for looking up detailed train connections:
http://www.hyperdia.com/

Use hyperdia.com inputting MASUDA as the passing station.
If you take shinkansen to Shin-Yamaguchi, there are Oki LTD Exp. direct to Matsue.
Or via Hagi w/ many transfers.

Is it possible to buy a 5-day JR West Rail Pass to go from Hakata to Osaka, but by way of Matsue?

No, Matsue is not covered by any JR West Pass. The only pass that would cover such a journey is the nationwide Japan Rail Pass.

I bought a Japan Rail Pass to go from Fukuoka/Hakata to Matsue, and then to Kyoto via Okayama; but I cannot find a train from Okayama to Kyoto that is not a Nozomi train, which the pass is not good for. I looked on Hyperdia. Is there a way from Okayama to Kyoto using the Japan Rail Pass?

I cannot find a train from Okayama to Kyoto that is not a Nozomi train, which the pass is not good for. I looked on Hyperdia. Is there a way from Okayama to Kyoto using the Japan Rail Pass?

Of course.

When using Hyperdia you should choose the "Search Details" option, and untick "Nozomi". This should give you plenty of results.

There are some direct Hikari trains. For example today there is the 7:36am Hikari, 8:21 Hikari, 9:27, 10:26, 11:26, 12:26, 13:26, etc. etc.

Alternatively, you can take one of the Hikari/Sakura/Kodama that go as far as Shin-Osaka and then change there for Kyoto, either using another Shinkansen, Haruka, or one of the Special Rapid trains.

Enjoy your trip!