3. You should have a Trik-L-Start as Winnebago started putting them as standard in their diesel pushers in the 2006 model year.
A Trik-L-Start will charge the chassis (engine) batteries while you are plugged into shore power by "stealing" a bit of charge from the house batteries. So if you do leave your coach plugged in, both house and chassis batteries should be kept charged.
I've attached the Winnebago announcement as to when they started putting Trik-L-Starts in their diesel pushers.
To make sure you do have one, look in you power cord compartment or under the hood behind the electrical door and see if you have something attached to the panel that looks like this:
ETA: The attached PDF kind of contradicts itself as it says that "all" 2006 diesel pushers will have the Trik-L-Start but then goes on to imply that only the P-series (Journey) and S-Series (Vectra) will have it. It doesn't mention the Tour. So we'll have to let a Tour owner answer this.