To 1: The pressure in a solid is the isotropic part of the strain tensor, which is extensively tabulated ( ask an mechanical engineer of your choice). It changes with T and density. Anyhow, in a solid body the expression pV in the definition of enthalpy should be replaced by stress*strain. The reference of choice of the physicist is Landau Lifshetz, elasticity theory.
To 2: Because 1 atm refers to internal pressure.
To 3: See 1
To 4: Not everything in Wikipedia is correct.
But the most important point: The easiest way to measure the internal pressure is in mechanical equilibrium situations, where internal and external pressure have to coincide. This is done e.g. in diamond anvil cells up to very high pressures. So it is easy to measure the pressure of a solid body e.g. as a function of density and temperature. This equation of state between pressure, density and temperature you may use to calculate internal pressure in more general situations, just like you use pV=nRT to calculate the internal pressure of an ideal gas e.g. during the explosion in a motor.