When you say idle, do you mean engine running idle or just ignition on ? Either way I don’t think it’s normal to have the bike shut off. As for the seat, I finally went to the dealer and got the DP comfort seat. Love it! Huge difference in seat grip + small/moderate difference in overall cushiness.
Okay, so there is something that has been explained to me that seems to be a general and common issue. The dash seems to get confused when the gear is in Neutral (N), it will remain at 1st gear. Some have said they can get it back to N by turning the bike off, then on again. Others say they just move their bike back and forth at a stop. For me, it just seems to randomly show the correct gear when it wants to.
Now, my point is that I have noticed something and re-tested my theory and found it to be factual. Ducati's will shut off when the kickstand is down and the gear is on anything but N. To test this, have the bike parked and motor off, but only the dash on. Then, switch the gear to anything but N. Now, when you press the start button you'll notice it won't start. Now, if you did all of this, but had the gear on N, then the bike will start when you press the push start button.
What this says is that when I am warming up the bike, and it randomly shuts off, that's because the computer thinks I've just switched the gear to 1. I was going crazy trying to figure this out, but noticed the dash kept changing the gear from 1 to N, and back and forth. All of this while the motor was shut off. So, not a big deal, but definitely something to note so you don't get scared when this happens.
Got the DP comfort seat from a member off this site too, and it's amazing! My ass and family jewels feel comfy on my commute to work (50mi one way).