I am studying for the B737-300/900 typerating.

My question is. Do I need to know all the dimensions and different weights for each model?

Not for the test.

Turning circle is very useful to know. A question that normally comes up is what makes the largest arc when turning? Nose, tail, wing etc. On the second part of the exam loadsheet, performance etc, you should be given the max TO/Landing weight. They do vary between individual aircraft. Hope this helps.