Re: Kessler Syndrome
In general, there would be a range of speeds and directions among the debris. Some would be steeply enough pitched and/or slowed enough to go deep enough into the atmosphere to be deorbited quickly. Others would, as you say, be faster than local circular-orbit speed, *but* from LEO circular-orbit speed to escape speed(1) is an increase of something like +50%, so actual escapes are unlikely.
So there would be a wide range of debris scattered "forward" from the collision (except in the case of a retrograde-prograde(2) impact, where all bets are off, but there would be a significant loss of speed), and some fraction of this debris would be at non-zero orbital inclinations and/or orbital eccentricities, and so would cross/touch the existing equatorial plane at significant delta-V and pose a significant risk to other satellites.
And yes, there have been collisions between satellites where the debris was tracked afterwards.
(1) It's a speed, not a velocity. Unless the path in a particular direction actually intersects the primary or some other orbiting body, it doesn't matter which direction an object that exceeds the escape speed travels - it *will* escape.
(2) Prograde: revolving(3) in the same direction that the primary rotates. Retrograde: revolving in the opposite direction to the one in which the primary rotates. A retrograde-prograde collision, then is head-on or close to it, and takes place at a much higher closing speed than a same-grade collision.
(3) Revolve: said of orbiting bodies, and describes their motion around the primary. Rotate: said of bodies in general, and describes their motion around their own axis.