Its my understanding that when your drifting with no acceleration the batteries are recharging. I did plently of that on the trip. If that is the case, why would the batteries need recharging after my trip?

What level does the batteries have to be in for the engine to remain on, after stopping, to recharge the batteries? Where can I see this level?

 

The battery runs between (guessing here) 99% and ~20-30% charge.
When it gets to the lower level, the computer turns on the engine to protect the battery.
You can coast down Mount Everest and be at full charge, then sit in traffic for five or ten minutes with the AC on and you will be at the lower band.
Don't worry about it, it's normal.
If you want to see it, press the DISP button until you get to the display showing the battery/wheels/engine indicator (non-NAV version).

 

Simple, the wheels have to be rolling to get any gas mileage. Even when coasting and the engine is at idle at 900 rpm you will still have a miles per gallon reading.

Once you stop if the engine is running you may see a 0 mpg (zero) Hold you foot steady on the brake and the engine should shut off within maybe 8 or so seconds. That one feature will save your gas over other the gas powered cars.