Hi,
"Analog Design Essentials" - W Sansen
"Analysis and Design of Analog Integrated Circuits" - Gray, Meyer, et al
"Modern Techniques for the Design of BJT OP Amps" by Sedra in his Microelectronic Circuits (chapter 13)
I couldn't do the calculations for you, but having found the first book myself, and followed recommendations of EDA members in other similar/related posts to read the other two books, I believe that if you search these books for the formulas you need you will be able to begin to answer your own questions quicker than you might think. Even so, I hope some-one else is able to give you a more useful answer for the time being.
As far as I recollect, the formulas, "simplified" models, etc., and examples are in the second book, and introduced in the first in the list; both discuss calculating input impedance and gain for different architectures, and both definitely analyse two-stage amplifiers (both BJT and MOS).
It might be nice to know if you are expected to invent the transistors based on the requirements or use mass-produced devices.
Good luck!
Sorry I can't be of more help.