Automatic delineation and detection of the primary tumour (GTVp) and lymph nodes (GTVn) using PET and CT in head and neck cancer and recurrence-free survival prediction can be useful for diagnosis and patient risk stratification. We used data from nine different centres, with 524 and 359 cases used for training and testing, respectively. We utilised posterior sampling of the weight space in the proposed segmentation model to estimate the uncertainty for false positive reduction. We explored the prognostic potential of radiomics features extracted from the predicted GTVp and GTVn in PET and CT for recurrence-free survival prediction and used SHAP analysis for explainability. We evaluated the bias of models with respect to age, gender, chemotherapy, HPV status, and lesion size. We achieved an aggregate Dice score of 0.774 and 0.760 on the test set for GTVp and GTVn, respectively. We observed a per image false positive reduction of 19.5% and 7.14% using the uncertainty threshold for GTVp and GTVn, respectively. Radiomics features extracted from GTVn in PET and from both GTVp and GTVn in CT are the most prognostic, and our model achieves a C-index of 0.672 on the test set. Our framework incorporates uncertainty estimation, fairness, and explainability, demonstrating the potential for accurate detection and risk stratification.