CE Amplifier Small-Signal Equivalent Circuit model confusion
They're skipping steps.  The first step in, for example, line B is: 
$$(v_b - V_i)\frac{1}{R_s} + (v_b - v_e)\frac{1}{r_{\pi}} = 0$$ 

If you then note that \$\frac{1}{R_s \parallel r_{\pi}} = \frac{1}{R_s} + \frac{1}{r_{\pi}}\$, can you see how this can be rearranged to get what they have?  Does it look more like the KCL that you're familiar with?

\$V_i\$ is not "shorted as in small signal analysis" because this is small-signal analysis, and you should assume that \$V_i\$ is just the AC component of the actual voltage on the base.