Effect of dilution on weak acids pH
Whatever the nature of the acids, weak or strong, dilution of an acidic solution produces an increase of pH. The dissociation coefficient may increase, but the pH will always increase. The expression &quot;like a Y letter&quot; is pure fantasy.
Your calculations about acetic acid are correct. Just a small remark : in the second part, you say :&quot;if  you double the volume&quot;. It should be stated that this operation is made by adding pure water. In this case, the total concentration of acid is divided by 2. Surprisingly, the concentration of $\ce{H+}$ is not divided by $2$ : $\ce{[H^+]}$ = $2.99 ·10^{-3} mol L^{-1}$. So it has been divided by $√2$ (and not by $2$).
Now, let's speak about the number of moles. During the dilution, the total number of moles of acetic acid has not changed, but the total number of moles of $\ce{H^+}$ has slightly increased during the dilution, which means that the acid is more dissociated in the diluted solution.