No LSD will not help chirps, it might actually increase it, cos both wheels will be distributing the force evenly, and you can put better power to the ground.

Also get a 4 wheel alingment and it should tell you if any caster is out. i believe that Pedders have a shock testing unit for a few dollars which will test your suspension and bushes for any other problems.

As for pulling to the side, which roads are you testing on or are they perfectly flat drag strips? Most roads are not flat so depending on when the tyres get grip they will pull a certain direction.