This paper proposes an approach for optimizing a Convolutional BeamFormer (CBF) that can jointly perform denoising (DN), dereverberation (DR), and source separation (SS). First, we develop a blind CBF optimization algorithm that requires no prior information on the sources or the room acoustics, by extending a conventional joint DR and SS method. For making the optimization computationally tractable, we incorporate two techniques into the approach: the Source-Wise Factorization (SW-Fact) of a CBF and the Independent Vector Extraction (IVE). To further improve the performance, we develop a method that integrates a neural network(NN) based source power spectra estimation with CBF optimization by an inverse-Gamma prior. Experiments using noisy reverberant mixtures reveal that our proposed method with both blind and NN-guided scenarios greatly outperforms the conventional state-of-the-art NN-supported mask-based CBF in terms of the improvement in automatic speech recognition and signal distortion reduction performance.