The spin effect of electrons/positrons ($e^-$/$e^+$) and polarization effect of $gamma$ photons are investigated in the interaction of two counter-propagating linearly polarized 10-PW-class laser pulses with a thin foil target. The processes of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production based on spin- and polarization-resolved probabilities are implemented into the particle-in-cell (PIC) algorithm by Monte Carlo methods. It is found from PIC simulations that the average degree of linear polarization of emitted $gamma$ photons can exceed $50%$. This polarization effect leads to reduced positron yield by about $10%$. At some medium positron energies, the reduction can reach $20%$. Furthermore, we also observe that the local spin polarization of $e^-$/$e^+$ leads to a slight decrease of the positron yield about $2%$ and some anomalous phenomena about the positron spectrum and photon polarization at the high-energy range, due to spin-dependent photon emissions. Our results indicate that spin and polarization effects should be considered in calculating the pair production and laser-plasma interaction with the laser power of 10-PW class.
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