The electric motor generator is directly connected to the motor like a flywheel, before the clutch, so it is always engaged. Electronics sensors and computer tell it when to charge the battery and when to act like a motor and assist the gas engine to power boost.

You drive the 5 speed just like any other 5 speed, just drive more conservatively to gain additional mileage. I believe that you have to have it in neutral when stopped for the motor to stop. This forum is full of hints on how to obtain better mileage.

You need to have the ECON button lit/engaged and AC in AUTO modes to make auto stop work.

If car is less than 36 months old and your mileage is correct, you seriously need to consider a Honda extended warranty availabe at any Honda dealer since this is a used car and you might not know the history/operation of previous owner. Negotiate for the low price by contacting different dealers. One problem could make the cost of warranty worthwhile.
Good luck