This paper focuses on the problem of sensing throughput optimization in a fading multiple access cognitive radio (CR) network, where the secondary user (SU) transmitters participate in cooperative spectrum sensing and are capable of harvesting energy and sharing energy with each other. We formulate the optimization problem as a maximization of the expected achievable sum-rate over a finite horizon, subject to an average interference constraint at the primary receiver, peak power constraints, and energy causality constraints at the SU transmitters. The optimization problem is a non-convex, mixed integer non-linear program (MINLP) involving the binary action to sense the spectrum or not, and the continuous variables, such as the transmission power, shared energy, and sensing time. The problem is analyzed under two different assumptions on the available information pattern: 1) non-causal channel state information (CSI), energy state information (ESI), and infinite battery capacity and 2) the more realistic scenario of the causal CSI/ESI and finite battery. In the non-casual case, this problem can be solved by an exhaustive search over the decision variable or an MINLP solver for smaller problem dimensions, and a novel heuristic policy for larger problems, combined with an iterative alternative optimization method for the continuous variables. The causal case with finite battery is optimally solved using a dynamic programming (DP) methodology, whereas a number of sub-optimal algorithms are proposed to reduce the computational complexity of DP. Extensive numerical simulations are carried out to illustrate the performance of the proposed algorithms. One of the main findings indicates that the energy sharing is more beneficial when there is a significant asymmetry between average harvested energy levels/channel gains of different SUs.