Kyushu Shinkansen to Kagoshima

1 Is the timetable for the new Kyushu shinkansen - to Kagoshima - available yet? Have been trying to find it on line but no success so far.
2 What would be the latest time I can leave Kagoshima to get back to Tokyo the same day?
3 Presumably I can use the JR Pass on the newly opened section of the Kyushu shinkansen?

Is the timetable for the new Kyushu shinkansen - to Kagoshima - available yet?

Yes.

In Japanese:
http://kyushushinkansen.com/cms/wp-content/themes/jr-sakura/images/tim...

The English timetable websites Hyperdia and Jorudan have not been updated yet.

2 What would be the latest time I can leave Kagoshima to get back to Tokyo the same day?

I believe you would have to catch the 16:34 Sakura train, assuming you use the Japan Rail Pass.

3 Presumably I can use the JR Pass on the newly opened section of the Kyushu shinkansen?

Yes, except on the Mizuho trains:
http://www.japan-guide.com/news/0017new.html

Uji must mean this:
http://www.japan-guide.com/news/0017.html