In this paper, we investigate a fluid antenna relay (FAR)-assisted communication system with hybrid relaying scheme selection. By leveraging statistical channel state information (CSI) and distribution characteristics of fluid antenna system (FAS), we approximate the outage probability (OP) with different relaying schemes utilizing a Gaussian copula-based method. Each relay node follows the OP-minimized principle to choose the forwarding schemes. To reduce self-interference and avoid multi-user interference, half-duplex relays and frequency division multiple access schemes are considered, respectively. On this basis, we formulate a sum-rate maximization problem to mitigate the rate loss introduced by the half-duplex mode. To solve this problem, we first transform the original nonconvex problem into a power control optimization problem by obtaining the closed form of bandwidth allocation and substituting it into the original problem. Then, we solve the power control optimization problem with a low complexity method. Simulation results verify the effectiveness of our proposed algorithm to improve the sum rate of the system.