Rate-Splitting Multiple Access (RSMA) is a flexible and robust multiple access scheme for downlink multi-antenna wireless networks. RSMA relies on Rate-Splitting (RS) at the transmitter and Successive Interference Cancellation (SIC) at the receivers. In this work, we study the performance of RSMA in the scenarios related with the important core services of New Radio (NR) and 6G, namely, enhanced Ultra-Reliable and Low-Latency (URLLC) and enhanced Mobile Broadband Communications (eMBB). We present the optimal system designs employing RSMA that target short-packet and low-latency communications as well as robust communications with high-throughput under the practical and important setup of imperfect Channel State Information at Transmitter (CSIT) originating from user mobility and feedback latency in the network. We demonstrate via numerical results that RSMA achieves significantly higher performance than Space Division Multiple Access (SDMA) and Non-Orthogonal Multiple Access (NOMA), and is capable of addressing the requirements for enhanced URLLC and eMBB in 6G efficiently.