My wife's truck also dies when cold if you get off the throttle too fast. And you also have to give some throttle for an immediate start. My Chevy on the other hand has never died by chopping the throttle, and starts without throttle if you so much as sneeze on the ignition. Many Many people have to give a little throttle for an immediate start. Bumping the idle will prob cure all your ills, but they really aren't that out of the norm.Bump the idle up if the stalling when cold bothers you.
otherwise normal for a low idle.
Using pedal to start is normal.