Why at constant pressure and temperature Gibbs energy change of a process can be negative?
The relation $dG = VdP - SdT$ implies that the Gibbs free energy of the system depends only on the two variables $T$ and $P$, e.g., as in the case of a single-component gas consisting of a fixed number of molecules. For such systems, the macrostate is completely determined if $T$ and $P$ are given; nothing can change further.

On the other hand, suppose that there is an additional parameter $X$ describing the system and that $X$ is not fixed. Then, according to the second law of thermodynamics, the system, being at constant $T$ and $P$, self-adjusts $X$ in such a way that $G$ is minimized.

In case there exist multiple species that can undergo a chemical reaction, $X$ could be a measure of how far the reaction has proceeded. The condition $\partial G/\partial X = 0$ gives the well-known law of chemical equilibrium.