This sounds like an electrical problem.
Look for loose grounds,dirty battery connections,loose plug connections,and corrosion around any electrical connection.
With my limited experience I'm going to say there is a loose connection somewhere fairly close to the battery.The reason I think this is because of the seemingly unrelated list of problems.If it was only the idle or the transmission I would say there is a bad sensor somewhere.With no codes showing up I'll stick with the loose connection.
The sensors are getting faulty information through crazy voltage changes and forwarding this information to the computer.The computer then tells the functioning system to do something that it isn't supposed to do and you have the transmission shifting at improper times or the engine racing away.
If you can get a Haynes or Chiltons manual they will have schematic diagrams of the electrical system.You could use this to maybe find a common connection for some of the faulty systems.They are only around $20 and have a lot of good info.
Here's a good link also.
http://www.allpar.com/