Regarding Darlington pair problem
The emitter current is not 1.98V/100Ohms. From the wording of the problem the darlington pair is sitting above the resistor (between the positive rail and the resistor). To get the emitter current Ie=Ib+Ic. To calculate the load current subtract the voltage drop from the darlington pair, and divide by the load resistance: I_Load=(V_Supply-V_DarlingtonDrop)/R_Load. That gives you the emitter current. From there you can calculate the base current using the usual darlington pair equations to write the collector current in terms of the base current Ic=(B1+B1B2+B2)Ie, and substitute into Ie=Ic+Ib. This site contains some useful tutorials on the subject.