(A) in Kumano Region
In Kii-Tanabe, the bus depot is next to the station, so try to get a hotel close by, especially if you are going to get on the 6:24 AM Ryujin Bus to Hongu Taisha. If you are a later sleeper, you could stay in Shirahama and catch the bus from there. Here is a link to bus timetables in the Kumano region in English:
http://www.tb-kumano.jp/en/transport/bus/I think that it is a good idea to visit one of the Onsens around Hongu Taisha. I usually stay at the Hotel Urashima in Katsuura, which is a resort with Hot Springs Sea Caves. It is a different atmosphere than an Onsen, which you may or may not like. Watching the Sushi carving demonstration is also fun.
The Limited Express train from KiiKatsuura (a station near Nachi Taisha) to Shin-Osaka is about 4 hours. The Shinkansen train from SHin-Osaka to Kagoshima is also about 4 hours long, and you may have as much as a one hour wait between trains (Lunch or Dinner). I would not short yourself on the final day at Nachi Falls and rush off to catch a train. I would consider staying in Kii-Katsuura overnight, or, just try to make it to Shin-Osaka. This would break up the trip to Kagoshima into two 4 hour train rides on different days.
(B) Overnight trains
A night train to Kagoshima does not exist.
The problem with the night train idea, is:
It works better going from Kagoshima to Tokyo.
The actual night train is the Sunrise Isumo/Sunrise Setto, which are two trains that join together in Okayama. The two linked trains then go to Tokyo.
You can catch the 6:29 PM Shinkansen Sakura 572 from Kagoshima-Chuo to Okayama, arriving at 10:00 PM. You will have 33 minutes to board the nighttrain before it takes off at 10:33 PM.
For this reason, I would put the Hot Springs visits to between Kumano and Kagoshima.
(C) Yakushima
If you are renting a car for Yakushima, does that mean that you will not be backpacking to mountain huts? Do you want the 2 day (one night) bus tour information? This could be extended to additional days with a car rental.
There are specific Jetfoils to take that dovetail well with the Kotsu bus sightseeing tours. The bus is set to arrive about 20 minutes after the Jetfoil docks, will take you and your luggage on a tour, and then drop you off at your hotel. The second tour pick you up, and drops off at a port about 20 minutes before the Jetfoil departs. The first bus makes for an easy day, and lets you get you rental car the following day.
The information ofr this is at the Yaku Monkey website I already gave you.
Is this information still helping you?