Can independent properties be related to each others simply by using a constant which can compensate for units problem?

"for example we use inert gas equation for relating pressure , temperature , volume , but these properties are dependent on each other now the question is about independent properties"

I believe you are referring to the ideal gas equation, PV = nRT.

As for independent properties (or perhaps "variable"?), I have never come across an experiment wherein all variables involved were independent, and then related to each other by a certain constant. As far as I know, an independent variable (or property) is always accompanied by a dependent variable. Properties that are independent of each other will have no effect whatsoever if one would try to correlate these properties. For example, I would not be able to correlate the pressure, temperature and volume of an ideal gas if all three were independent of each other. Same goes for density of a material if mass and volume were not related to each other in any manner.

Yes you can, but you have to explain your relationship in our real world.