1. In general, acid + $$\ce{H_2O} \rightleftharpoons$$ base + $$\ce{H_3O^+}$$
2. It is called the Henderson-Hasselbach equation $$pH = pK_a + \log\frac{[base]}{[acid]}$$
3. I believe the equilibrium constant for a such a neutralisation would look like $$K_n = K_aK_b\frac{1}{K_w}$$