What is the effect of adding HCl on a certain solution at equilibrium?
You are absolutely correct. Adding $\ce{HCl}$ adds protons to the mix, which you can imagine as applying pressure on the right-hand side, which means that the reaction will shift backwards slightly and the acetate concentration will decrease. For $\ce{NaOH}$, you also need to consider the underlying equation:

$$\ce{H2O &lt;=&gt; H+ + OH-}$$

which will be shifted to the left by additional hydroxides. This means that the overall proton concentration decreases and you can imagine that as lifting a weight from the right-hand side: The reaction will shift forwards.