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The system for

$\mathrm dG=\mathrm dH-T\,\mathrm dS$

is a constant temperature and pressure throughout the process, only volume work is possible and it is in thermal equilibrium with the surrounding. Is that right? Are there any other constraints?

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The only restriction on your equation is that the system is at constant temperature. The system can be open or closed, the pressure does not have to be constant, and any type of work is allowed.

Let's start with the basic definition of G in terms of H, which is completely unrestricted:

$$G \equiv H-TS \Rightarrow dG = dH - d(TS) = dH -TdS -SdT$$

Then, to get your equation, the only restriction we need to add is constant $T$:

$$dG= dH -TdS$$

Why, then, might you be associating this equation with the more extensive restrictions of constant $T$ and $p$, and no non-$pV$ work? I suspect it's because, to use $dG = dH -TdS = 0$ as a condition for equilibrium, these other restrictions are required. For more on this, see the end of my answer at What is wrong in this argument that dG must always be zero?

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