The paper studies a wireless-powered full-duplex non-orthogonal multiple access (NOMA) system with one base station and two groups of near and far users, where the near users can be regarded as the self-energy recycling relays to assist the far users. In particular, the locations of the near and far users are modeled as the uniformly distributed and homogeneous Poisson Point Process respectively. From the beneficial perspective of the near users, we propose a novel power allocation scheme, which can utilize the partial channel state information to switch the transmission mode dynamically between cooperative NOMA and non-cooperative NOMA. Further, since the users’ locations have a significant influence on our proposed power allocation scheme, three different user selection strategies namely random near user and random far user (RNRF), optimal near user and nearest far user (ONNF), and optimal near user and farthest far user (ONFF) are investigated to carry out NOMA pairing. Firstly, the RNRF allows all of users to communicate with the base station by a fair opportunity compared to the others strategies, and then a two-stage user selection method is proposed by considering the actual states of near users to determine an optimal near user who can maximize the outage performance of far user for ONNF and ONFF strategies. In addition, outage probabilities, diversity orders, and system throughputs are derived to characterize the performance of three strategies. Finally, numerical results are shown to verify that not only our proposed power allocation scheme can improve the quality of service of near users but also user selection strategies can fully exploit multi-user diversity in comparison to the existing work.