There are opposed thrusters, but I assume that in atmosphere and under parachute canopy it’s harder to make sure they are perfectly opposed.

Heating likely plays a role as well.

I am not a rocket engineer, but I have read How Apollo Flew to the Moon and Ignition!: an informal history of liquid rocket propellants, both of which cover these issues. Highly recommended.

The short bursts are just the period of the control cycles. Control cycle starts, loop sees error, commands thrust; next control cycle starts, loop sees error is nulled (or in deadband), commands no thrust.