The crucial point is that right angle, EFG. Because of that the two angles AFE and GFB are "complementary"- the measures of the three angles, AFE, EFG, and GFB, add up to 180 degrees because they form a straight line and since EFG is a right angle, AFE and GFB add to 90 degrees.
And then, look at right triangles EAF and FGB. Angle EFA is complementary to AEF and FGB is complementary to GFB. That, together with the fact that AFE and GFB are complementary, shows that EFA and FGB are congruent.
For (b) you need the additional given information, that "EFG is an isosceles triangle". That is, sides EF and FG are congurent. Then use "ASA".
For (c), notice that drawing horizontal and vertical lines through M divides the square into 4 smaller but identical squares.