In public safety communications, direct mode communication is essential to keep first responders connected, especially when there is no network coverage. Direct mode communication is supported in Third Generation Partnership Project (3GPP) Long Term Evolution (LTE) via Sidelink (SL). With 3GPP advancing from LTE to Fifth Generation (5G), in this study we explore new features brought by 3GPP 5G New Radio (NR) SL and evaluate its support of direct mode communications. This study focuses on five major topics that are essential to public safety communications over 5G NR SL: resource management, physical layer, capacity, Quality of Service (QoS), and LTE/NR coexistence. First, on resource management, we analyze the supported mapping between applications and SL resources, control of communication type (unicast, multicast, and broadcast), together with SL physical resource pools. We then identify several areas for further research, including resource provision for different types of applications and management of concurrent applications. Second, on physical layer, we highlight NR new features that are expected to improve performance, including NR's flexible numerology, feedback channel, advanced channel coding mechanism, and channel sensing. Third, on capacity, we use maximal achievable data rate as the measure, and analyze in detail factors that impact NR SL capacity, including various parameters and overheads. We then study SL capacity under various NR operational configurations and device capabilities. Using Band n14 for numerical analysis purpose, we also analyze LTE capacity for comparison purpose, and further quantify NR capacity improvement over LTE brought by each of the NR new features. Fourth, on QoS, we notice that compared with the relatively simplified LTE QoS operations, NR SL has much enhanced QoS support by inheriting various Uu QoS operations and by introducing new features, such as the new layer Service Data Application Protocol (SDAP) and the new parameter Range. The NR SL QoS parameters are also backward compatible with QoS parameters of LTE Proximity Services (ProSe). We describe these enhancements in detail, as well as the ongoing 3GPP standardization efforts in supporting public safety communications. Fifth, on LTE/NR coexistence, we address the transition from LTE to NR before re-farming the full bands. We discuss in detail Dynamic Spectrum Sharing (DSS), such as the exchange of configurations between LTE and NR, then point out the limitation in supporting sharing over SL, and possible solutions and 3GPP standard efforts. Last but not least, we provide an overview of ongoing 3GPP study items and work items related to the NR SL, including NR ProSe, direct discovery, direct communication, and UE-based relays, as well as enhancements to the NR SL power efficiency, reliability, and latency. While our study shows promising potential performance improvement on direct mode communications from 5G NR SL over LTE, the study also identifies its limitations. Ad-dressing these limitations to better support first responders, plus developing measurement tools to quantify performance, will be our next steps.