A three-stage approach is proposed for speaker counting and speech separation in noisy and reverberant environments. In the spatial feature extraction, a spatial coherence matrix (SCM) is computed using whitened relative transfer functions (wRTFs) across time frames. The global activity functions of each speaker are estimated from a simplex constructed using the eigenvectors of the SCM, while the local coherence functions are computed from the coherence between the wRTFs of a time-frequency bin and the global activity function-weighted RTF of the target speaker. In speaker counting, we use the eigenvalues of the SCM and the maximum similarity of the interframe global activity distributions between two speakers as the input features to the speaker counting network (SCnet). In speaker separation, a global and local activity-driven network (GLADnet) is used to extract each independent speaker signal, which is particularly useful for highly overlapping speech signals. Experimental results obtained from the real meeting recordings show that the proposed system achieves superior speaker counting and speaker separation performance compared to previous publications without the prior knowledge of the array configurations.