the first thing you need to do with buffer solutions is to write down your equilibrium. In the first question, the equilibrium is:
NH4(+) + H2O <--> NH3 + H3O(+)
Then you know the ratio of NH3 and NH4(+) in the solution. In this case, this is 1 --> Ka = [H3O(+)] or pKa = pH
when we add 12 mL 0,20 M HCl, we add 12 * 0,2 = 2,4 mmol HCl, thus 2,4 mmol H3O(+). This will react with the NH3. You know the volume of your buffer and the concentrations of NH3 and NH4(+) (0,1 * 125 = 12,5 mmol), thus finally we have 12,5 - 2,4 = 10,1 mmol NH3 and 12,5 + 2,4 = 14,9 mmol NH4(+)
thus then we get: pKa = pH + log 10,1/12,4