So the first part of the question is the rxn between the acetate and the HCl. We see that we actually neutralise exactly half of the acetate, so we have 0.5 mols of acetate and 0.5 mols acetic acid. ie equimolar amounts of weak acid and its weak conj. base (buffer). You can calculate the Ka of acetic acid using an ICE table, but since the concentration of acetate and acetic acid are so close, we know that pH = pKa. Now that we know the Ka of the acid, we can use this to construct another ICE table, now using the fact that our solution is 1L in volume. Our initial conditions are 0.05M for acetate and acetic acid (easier to consider the system prior to any shifting) and 0M for the H+. You can then calculate the shift since we know the Ka and thus we can find the pH of the solution, but since our shift will be very very small, we recognise that the concentration of acetic acid and acetate will be very similar, so once again [H+] = Ka, and thus pH = pKa, ie pH = 4.8.
It may be easier to see this when you write out the equilibrium expression