Is this rail itinerary possible?

Hi,
Nearly all the places you mention you can reach by rail. Kyoto to Matsumoto is just over 3 hours with a good connection. To Takayama it is 3 hours 15 minutes. To Kamikochi you take the train to Matsumoto, then take a non-JR train and then a bus, both of which you need to buy tickets for, and adds another 90 minutes to get to Kamikochi. You could however go to Takayama, and then pay for a one hour bus ride to Kamikochi.

But Matsumoto to Kumamoto Stn. would be long - about 7 hours 20 minutes, with at least 2 train transfers. And then more to Aso.

If you'd like to check regular fares and schedules, you can go to Hyperdia and just plug in your starting point and end point, plus date/time that you like. But be sure under "More Options" to deselect "Nozomi..." since you can't ride that on the Pass.

Kumamoto is famous for its castle, and beautiful Suizenji Garden. It's unclear why you choose that as a destination - it has its good sights, but other places like Nagasaki and Fukuoka have more variety to offer. And unfortunately, the crater area around Mt. Aso is still closed and looks likely to stay that way for some time due to volcanic gas emissions. Kumamoto Stn. to Mita will take almost 7 hours on the train.

Best of luck.