While I agree that these would be in a lower orbit, if they are low enough that debris would fall quickly then so would satellites. Debris doesn't know it's debris and so it should fall when the satellite did not.
Yes, some satellites can self-boost with ion drives giving them longer life in lower orbits, but they can't do that very often or for very long due to reaction mass limits. You're still talking about orbits where debris would last years.
No, debris in the same orbit would fall much more quickly than satellites, due to the square/cube difference, a larger piece gets slowed much less than many smaller pieces with the same combined mass.
Also, "the same orbit" is the best/worst case scenario, since after an impact any new orbit still passes through the point of impact, but if the new orbit is more elliptic than the original (which most likely was close to circular), then it has a lower perigee, where most of the drag occurs, and thus would get dragged down faster than in the original orbit.
If a satellite is in a low orbit that needs re-boosting every few years, then the debris from its destruction would get cleared out in weeks or months.
No, these defenses would be in low orbit, and low orbits are rapidly self cleaning. Kessler Syndrome is only for high orbits.
There no reason for an attacking missile to go into a high orbit, they would stay pretty low.