Question

is the Earth a closed or open system(thermodynamics)

Answer 1

While individual components of the Earth may be considered by definition an open physical system (where highly-localized decreases of entropy may intermittently occur), the Earth's climate system including land, oceans, and atmosphere in total are considered to be a closed thermodynamic system, for which the 2nd Law of Thermodynamics applies and requires total system entropy to always increase.