We report ALMA observations of NGC 1333 IRAS 4A, a young low-mass protostellar binary, referred as 4A1 and 4A2. With multiple H$_2$CO transitions and HNC (4$-$3) observed at a resolution of 0.25" ($\sim$70 au), we investigate the gas kinematics of 4A1 and 4A2... Our results show that, on the large angular scale ($\sim$10"), 4A1 and 4A2 each display a well-collimated outflow along the N-S direction, and an S-shaped morphology is discerned in the outflow powered by 4A2. On the small scale ($\sim$0.3"), 4A1 and 4A2 exhibit distinct spectral features toward the continuum centroid, with 4A1 showing simple symmetric profiles predominantly in absorption and 4A2 demonstrating rather complicated profiles in emission as well as in absorption. Based on radiative transfer modeling exercises, we find that the physical parameters inferred from earlier low-resolution observations cannot be directly extrapolated down to the 4A1 inner region. Possible reasons for the discrepancies between the observed and modelled profiles are discussed. We constrain the mass infall rate in 4A1 to be at most around 3$\times$10$^{-5}$ M$_{\odot}$ year$^{-1}$ at the layer of 75 au. For the kinematics of the 4A2 inner envelope, the absorbing dips in the H$_2$CO spectra are skewed toward the redshifted side and likely signatures of inward motion. These absorbing dips are relatively narrow. This is, like the case for 4A1, significantly slower than the anticipated inflow speed. We estimate a mass infall rate of 3.1$-$6.2 $\times$ 10$^{-5}$ M$_\odot$ year$^{-1}$ at the layer of 100 au in 4A2. (read more)