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Based on 3D compressible magnetohydrodynamic simulations, we explore the interactions between the magnetized wind from a solar-like star and a Mars-like planet – with a gravitionally stratified atmosphere – that is either non-magnetized or hosts a weak intrinsic dipolar field. The primary mechanism for the induction of a magnetosphere around a non-magnetized conducting planet is the pile-up of stellar magnetic fields in the day-side region. The magnetopause stand-off distance decreases as the strength of the planetary dipole field is lowered and saturates to a minimum value for the case of a planet with no magnetic field. Global features such as bow shock, magnetosheath, magnetotail, and strong current sheets are observed in the imposed magnetosphere. We explore variations in atmospheric mass loss rates for different stellar wind strengths to understand the impact of stellar magnetic activity and plasma winds – and their evolution – on (exo)planetary habitability. In order to simulate a case analogous to the present-day Mars, a planet without atmosphere is considered. Our simulations are found to be in good agreement with observational data from Mars Global Surveyor and Mars Atmosphere and Volatile EvolutioN missions and is expected to complement observations from the Emirates (Hope) Mars Mission, China's Tianwen-1 and NASA's Mars 2020 Perseverance mission. [ABSTRACT FROM AUTHOR]