What is pressure?

Pressure is force divided by area -or P = force divided by area

What is the difference between psi and psia?

Psia describes an absolute pressure per square inch that starts from a perfect vacuum. 

Psia is influenced by weather and elevation. 

A good frame of reference is at sea level there is 14.7-psia psi describes a relative pressure that starts from atmospheric pressure.  Therefore if you are on a mountain and the pressure vessel gage reads 1000-psi and relocate the pressure vessel to sea level the gage will read 1000-psi.  We can further say that at sea level there is 0-psi.  Example, when purchasing a new gage the pressure gage reads zero.We can now say psia is an absolute pressure reading, and psi is a relative pressure reading.  In most cases, psi is used on pressure vessels.

What is the difference between inches H₂O and inches of Hg?

There is little difference except they have to be converted.  Inches of  H₂O is more sensitive than inches of Hg because mercury is heavier than water. At sea level there is 407.1 inch H₂O  and 29.9 inches Hg at sea level.    

Should a pressure vessel have a pressure gage?

A.) Yes     B.) No

Answer

 A) Yes. 

In fact, the gage needs a siphon to keep hot vapors from damaging the bellows in the gage; otherwise, the gage becomes damaged and unreliable. If there are pulsation's are experienced in the vessel, then a snubber is needed, for no gage can handle that kind of abuse. The gage needs to have the proper graduated range [0-100-psi gage]. For instance a 100-psi vessel should have a gage graduated no higher than a 0-300-psi gage or no lower than a 0-150-psi gage.