Published by the American Astronomical Society.We present a statistical study of 180 dust continuum sources identified in 33 massive cluster fields by the Atacama Large Millimeter/submillimeter Array Lensing Cluster Survey (ALCS) over a total of 133 arcmin2 area, homogeneously observed at 1.2 mm. ALCS enables us to detect extremely faint millimeter sources by lensing magnification, including near-infrared (NIR) dark objects showing no counterparts in existing Hubble Space Telescope and Spitzer images. The dust continuum sources belong to a blind sample (N = 141) with signal-to-noise ratio (S/N) ≳ 5.0 (a purity of >0.99) or a secondary sample (N = 39) with S/N = 4.0-5.0 screened by priors. With the blind sample, we securely derive 1.2 mm number counts down to ∼7 μJy, and find that the total integrated 1.2 mm flux is 20.7 − 6.5 + 8.5 Jy deg−2, resolving ≃80% of the cosmic infrared background light. The resolved fraction varies by a factor of 0.6-1.1 due to the completeness correction depending on the spatial size of the millimeter emission. We also derive infrared (IR) luminosity functions (LFs) at z = 0.6-7.5 with the 1 / V max method, finding the redshift evolution of IR LFs characterized by positive luminosity and negative density evolution. The total (= UV + IR) cosmic star formation rate density (SFRD) at z > 4 is estimated to be 161 − 21 + 25 % of the Madau and Dickinson measurements mostly based on rest-frame UV surveys. Although our general understanding of the cosmic SFRD is unlikely to change beyond a factor of 2, these results add to the weight of evidence for an additional (≈60%) SFRD component contributed by the faint millimeter population, including NIR-dark objects.