1. You should provide the currents injected at each node, i.e., Ii (i = 1,2,3,4), or equivalently per-unit real and reactive powers for each node, i.e., Pi and Qi (i = 1,2,3,4). Or allow me to use the values used in page 11 of the pdf file (Example 11.3).
2. What do you mean by "a mathematical solution?" If you mean an analytic closed form solution, as the system of equations is nonlinear, I can think of two possibilities: i) the system has no closed form solution, ii) the system has a closed form solution, but very complicated to express. Therefore I suggest you to remove this item from project or consider the MATLAB iterations as an answer to this part (this is possible and simple).
3. The report is the combinations of above with some parts of pdf file.