I have a question regarding the demodulation of AM signals in radio systems (like car radio).

I know that in order to send the audio signal from the broadcasting station to users we need first to AM modulate it with fc and s(t) will be the modulated signal, so in frequency domain we send the audio signal to the passband around the carrier wave fc, the thing that bothers me is: at the receiver side after the Tuner selects the correct channel that the user want with a BPF do we need to move the selected signal s(t) to the baseband (frequency range around the audio signal) with a mixer and then pass it trough an envelop detector, or we can pass our bandpass signal s(t) straight to the envelop detector without down converting it to baseband?

By baseband, I assume that you meant the frequency range of the original message $$s(t)$$. Both mixing and peak detection bring the spectrum centered around $$f_c$$ to the original frequency range of $$s(t)$$. So you don't need both[1]; only one of them.