1. How do I know when to sketch a broken line and when to sketch a solid line with inequalities?

If the problem involves the signs ≥ or ≤ then use a SOLID line.

If the problem involves > or < then use a BROKEN line.

2. Is there always a question on linear programming in the Bursary examination?

There is never any guarantee on what questions will be in the Bursary exam. although there is usually a question on EITHER linear programming or exponential or power function modelling.