In this paper, we present a novel approach for joint activity detection (AD), channel estimation (CE), and data detection (DD) in uplink grant-free non-orthogonal multiple access (NOMA) systems. Our approach employs an iterative and parallel interference removal strategy inspired by parallel interference cancellation (PIC), enhanced with deep learning to jointly tackle the AD, CE, and DD problems. Based on this approach, we develop three PIC frameworks, each of which is designed for either coherent or non-coherence schemes. The first framework performs joint AD and CE using received pilot signals in the coherent scheme. Building upon this framework, the second framework utilizes both the received pilot and data signals for CE, further enhancing the performances of AD, CE, and DD in the coherent scheme. The third framework is designed to accommodate the non-coherent scheme involving a small number of data bits, which simultaneously performs AD and DD. Through joint loss functions and interference cancellation modules, our approach supports end-to-end training, contributing to enhanced performances of AD, CE, and DD for both coherent and non-coherent schemes. Simulation results demonstrate the superiority of our approach over traditional techniques, exhibiting enhanced performances of AD, CE, and DD while maintaining lower computational complexity.