I. The tabulated empirical data refer to a specific pressure and temperature. In that sense they are constant. Whatever pressure and temperature you're working at, ΔH°f(298K, 1 atm) has the same value. But the heat of formation at another temperature will not be the same (see below). This is important because when you use the equation for ΔG at a particular temperature, you must use the ΔH and ΔS values for that temperature, not 298K; e.g.
ΔG°(400K) = ΔH°(400K) - 400*ΔS°(400K)
Over a small temperature range, ΔH and ΔS usually don't vary much, so it is a reasonable approximation to use the 298K values at (say) 310K, but probably not at 400K.
These considerations apply equally to ΔG°, ΔH° and ΔS°, not just ΔG°. You can find tabulated values of ΔG°f(298K, 1 atm). But you can define a standard state for G, H and S at any temperature. There is no such thing as THE standard state.
II. Enthalpy and entropy vary with temperature, depending on the heat capacity. dH/dT = Cp and dS/dT = Cp/T. So if reactants and products have different heat capacities, ΔH and ΔS vary with temperature.
So dΔH/dT = ΔCp, where ΔCp = ΣCp(products) - ΣCp(reactants).
dΔS/dT = ΔCp/T
(In fact it is a bit more complicated, as Cp itself varies with temperature.)
(Note that to a first approximation this doesn't affect ΔG, as dΔG/dT = dΔH/dT - TdΔS/dT - ΔS = ΔCp - ΔCp - ΔS = ΔS.)
Another thing that affects ΔH° and ΔS° is phase changes; e.g. if a reactant has a melting point of 300K, then below this temperature the standard state is solid, and above 300K the standard state is liquid, so there is a step change in H due to the heat of fusion.