Some techniques that were educational or helpful:

3.3.4:
Since X, Y, and Z are Hermitian and their own inverses, and after verifying that Y = iXZ, we easily have the following using conjugate transpose operations and/or matrix inverses:
Y = -iZX
Z = -iXY
Z = iYX
X = -iYZ
X = iZY

3.3.9:
Okay to verify the behavior of an orthonormal basis under this transformation.  Also, Hadamard is its own inverse, so the second property follows immediately.

3.3.10:
Proof uses the fact that eigenvalues are +-1.

3.4.5:
Any state with real coefficients (on the X-Z axes equator in the Bloch sphere).

3.5.4:
Okay to verify the behavior of an orthonormal basis under this transformation.

3.6.6:
Use the fact that X(x) = (X(1))^x.