Is it permissible for a woman to play sports where there is no physical contaact such as badminton with a man while being in proper hijab?

If a woman is appropriately dressed and is wearing loose fitting, and while playing the different postures don’t reveal her body shape, and they don’t cross any Islamic boundaries like joke with each other, then technically it’s permissible. But honestly it’s quite difficult to observe all these conditions, hence it is not advised to play with the opposite gender.

Is it permissible for a woman to play sports where there is no physical contaact such as badminton with a man while being in proper hijab?

There is no problem if they can safeguard themselves from falling into haram (ie gazes etc)