Reconfigurable intelligent surfaces (RISs) have recently emerged as a promising technology that can achieve high spectrum and energy efficiency for future wireless networks by integrating a massive number of low-cost and passive reflecting elements. An RIS can manipulate the properties of an incident wave, such as the frequency, amplitude, and phase, and, then, reflect this manipulated wave to a desired destination, without the need for complex signal processing. In this paper, the asymptotic optimality of achievable rate in a downlink RIS system is analyzed under a practical RIS environment with its associated limitations. In particular, a passive beamformer that can achieve the asymptotic optimal performance by controlling the incident wave properties is designed, under a limited RIS control link and practical reflection coefficients. In order to increase the achievable system sum-rate, a modulation scheme that can be used in an RIS without interfering with existing users is proposed and its average symbol error ratio is asymptotically derived. Moreover, a new resource allocation algorithm that jointly considers user scheduling and power control is designed, under consideration of the proposed passive beamforming and modulation schemes. Simulation results show that the proposed schemes are in close agreement with their upper bounds in presence of a large number of RIS reflecting elements thereby verifying that the achievable rate in practical RISs satisfies the asymptotic optimality.