As a non-native-speeker, I'm having difficulties to understand difference between 'Education system' and 'Educational system'? Is 'Educational system' appropriate at all?
Educational - means something that educates, and it is an adjective
Education - is a noun. When used with objects as a determiner it means related to or about education.
In your concrete example education system refers to the schools, universities, etc. - the system consisting of different bodies that provide education. Though educational system can also be used to refer to the same entity, it is a more general phrase and any system that has an effect of making someone more educated can be considered educational, for example a piece of software that helps kids to learn something can be called educational system.