Orthogonal Time Frequency Space (OTFS) modulation has recently attracted significant interest due to its potential for enabling reliable communication in high-mobility environments. One of the challenges for OTFS receivers is the fractional Doppler that occurs in practical systems, resulting in decreased channel sparsity, and then inaccurate channel estimation and high-complexity equalization. In this paper, we propose a novel unsupervised deep learning (DL)-based OTFS channel estimation and symbol detection scheme, capable of handling different channel conditions, even in the presence of fractional Doppler. In particular, we design a unified plug-and-play (PnP) framework, which can jointly exploit the flexibility of optimization-based methods and utilize the powerful data-driven capability of DL. A lightweight Unet is integrated into the framework as a powerful implicit channel prior for channel estimation, leading to better exploitation of the channel sparsity and the characteristic of the noise simultaneously. Furthermore, to mitigate the channel estimation errors, we realize the PnP framework with a fully connected (FC) network for symbol detection at different noise levels, thereby enhancing robustness. Finally, numerical results demonstrate the effectiveness and robustness of the algorithm.