Visualizing dynamics of a two-level atom on the Bloch Sphere

I am trying to use the Bloch Sphere to understand how applying resonant sequences of $pi/2$ and $pi$ pulses changes the state of a two-level system initially in the ground state. Specifically, I am looking at whether I can get to any arbitrary pure state from the ground state in three separate cases:

a) Using a sequence of two resonant $pi/2$ pulses.
b) Using a sequence of two resonant $pi$ pulses.
c) Using a sequence of resonant $pi/2 to pi to pi/2$ pulses.

Each pulse can have a different phase $mathrm{Im}(Omega)$, and there can be any duration of time between the pulses, but all pulses are resonant: i.e. the detuning $Delta$ is zero. I am going to work on the Bloch sphere:

My intuition tells me a) should be possible, but I cannot get there through my reasoning. Initially the Bloch vector $mathbf{R}$ is pointing toward the $z$-axis, since we are starting from the ground state. The first $pi/2$ pulse with any phase brings the Bloch vector down to the equatorial plane since the precession vector $mathbf{W} = (mathrm{Re}(Omega), mathrm{Im}(Omega), Delta=0)$ lies in the $xy$-plane. Free evolution before the next pulse just makes the Bloch vector $mathbf{R}$ precess around the $z$-axis, meaning all equatorial states can be accessed. The second $pi/2$ pulse can have an arbitrary phase, so the vector $mathbf{W}$ can be anywhere on the equator. The pulse will cause a rotation of the $mathbf{R}$ clockwise about $mathbf{W}$, so we should be able to access any state in the lower hemisphere. But how do we get to the upper hemisphere? Will a suitable phase of the second pulse do the trick?

Likewise, I am confused about cases b) and c). I would appreciate any help or clarification.