Concerns have been growing over fake news and its impact. Software that can automatically detect fake news is becoming more popular. However, the accuracy and reliability of such fake-news detection software remains questionable, partly due to a lack of testing and verification. Testing this kind of software may face the oracle problem, which refers to difficulty (or inability) of identifying the correctness of the software's output in a reasonable amount of time. Metamorphic testing (MT) has a record of effectively alleviating the oracle problem, and has been successfully applied to testing fake-news detection software. This paper reports on a study, extending previous work, exploring the use of MT for fake-news detection software. The study includes new metamorphic relations and additional experimental results and analysis. Some alternative MR-generation approaches are also explored. The study targets software where the output is a real/fake news decision, enhancing the applicability of MT to current fake-news detection software. The paper also explores the impact of the prediction accuracy of the fake-news detection software on the MT process. The study demonstrates the validity and applicability of MT to fake-news detection software. The prediction accuracy of the software has a greater impact on MT experiments with greater changes between the source and follow-up inputs, and less dependence on prediction stability. Some possible factors affecting the experimental results are discussed, and directions for future work are provided.