Chemical Thermodynamic Functions I'm a high school student with basic knowledge about chemical thermodynamics. I have three questions regarding the thermodynamic state functions $H, S, G$. I have searched a lot in textbooks but they don't give the complete information as to whether the properties taken are that of the system or surroundings.

Q1):-Enthalpy is given by the formula

$H = U +PV$ . 
 What I want to know is that whether $P$ mentioned above is the internal pressure of the system or the externally applied pressure?

Q2):- The change in entropy is given by the formula
$\Delta S= $$\int_1^2$${\frac{dq_{reversible}}{T}}$. Is the temperature mentioned of the system or the surroundings. 

Q3)-On the same lines what temperature is taken to define the Gibbs free energy function:-$G=H-TS$.

Thanks in advance.
The three functions you mentioned are applicable only to thermodynamic equilibrium states of the system, for which the pressures and temperatures of the system and its surroundings match one another to within insignificantly small differences.  In the integral to get the entropy change (Q2), the same matching applies; that is, a reversible path consists of a continuous sequence of thermodynamic equilibrium states.

Note that, at the interface between the system and the surroundings, the temperature and pressure of the system always matches the temperature and pressure of the surroundings (irrespective of whether the system is at equilibrium).  It's just that, along an irreversible path of the system (for which the system passes through a sequence of non-equilibrium states), the pressure and temperature within the system vary with spatial position, and their average values (averaged over the volume of the system) do not match those of the surroundings at the interface.