This paper studies the multi-link multi-antenna amplify-and-forward (AF) relay system, in which multiple source-destination pairs communicate with the aid of an energy harvesting (EH)-enabled relay and the relay utilizes the power splitting (PS) protocol to accomplish simultaneous EH and information forwarding (IF). Specifically, independent PS, i.e., allow each antenna to have an individual PS factor, and cooperative power allocation (PA) i.e., adaptively allocate the harvested energy to each channel, are proposed to increase the signal processing degrees of freedom and energy utilization. Our objective is to maximize the minimum rate of all source-destination pairs, i.e., the max-min rate, by jointly optimizing the PS and PA strategies. The optimization problem is first established for the ideal channel state information (CSI) model. To solve the formulated non-convex problem, the optimal forwarding matrix is derived and an auxiliary variable is introduced to remove the coupling of transmission rates in two slots, following which a bi-level iteration algorithm is proposed to determine the optimal PS and PA strategy by jointly utilizing the bisection and golden section methods. The proposal is then extended into the partial CSI model, and the final transmission rate for each source-destination pair is modified by treating the CSI error as random noise. With a similar analysis, it is proved that the proposed bi-level algorithm can also solve the joint PS and PA optimization problem in the partial CSI model. Simulation results show that the proposed algorithm works well in both ideal CSI and partial CSI models, and by means of independent PS and cooperative PA, the achieved max-min rate is greatly improved over existing non-EH-enabled and EH-enabled relay schemes, especially when the signal processing noise at the relay is large and the sources use quite different transmit powers.