I leave mine in gear and put the parking break on if I am parked on a slope.

I understand leaving a car in gear in a traditional manual, but does leaving the SMG in gear provide the same benefit? If you are in 1st gear, with your foot neither on the brake or the gas, and on a hill sloping towards the rear of the car, the car will roll backwards, despite being in first. It is my understanding (though I could be wrong) that at low rpm's the SMG transmission "applies the cluth pedal" to prevent stalling, such that the car is essentially in neutral. This is why the car will roll backward, without stalling.
Does the car work differently when the the engine is not running? That is, does the care really stay in gear, or does it shift to "neutral" when you come to a stop?

I think that when the engine is stopped, the clutch is engaged, just like if you were driving a traditional manual. When the engine is running and you're in gear but stopped, the clutch is disengaged, just like you had the clutch pedal depressed.

Thanks Rudy. If so, there is a benefit to leaving the car in gear when parked on a slope.

Absolutely. If you don't leave it in gear on a slope, it will roll unless the emergency brake is set. Chime Buddy will fuss about it, too. :)

I leave my in gear also but will it cost problem if you leave it neutral??

In Gear and Parking brake for me. Habit, and then don't get the warning.

Usually N + ebrake, sometimes in gear + ebrake. My car sometimes jerks when the engine is shut down in gear :|

Yeah I noticed on mine that if its set to neutral that it chimes to sort of let you know that it wants to be in gear. I thought I was reading it wrong.

It chimes and it shows a picture of the car with arrows overhead to give the impression of the car rolling.