hmmmm, can’t help you with your door locks, although i have heard of this problem.
your stalling problem is most likely a vacuum leak… but it’s got nothing to do with downshifting.
usually rpm’s will drop below idle under hard braking, whether or not you’re in gear.
a shift is a shift…if you’re stalling while downshifting, then you should also be stalling while upshifting, unless your idea of downshifting is holding in the clutch and moving through the gears (ie. 4-3-2-1) while braking, without actually letting off the clutch to engage each gear.