In positron emission tomography (PET), attenuation and scatter corrections are necessary steps toward accurate quantitative reconstruction of the radiopharmaceutical distribution. Inspired by recent advances in deep learning, many algorithms based on convolutional neural networks have been proposed for automatic attenuation and scatter correction, enabling applications to CT-less or MR-less PET scanners to improve performance in the presence of CT-related artifacts. A known characteristic of PET imaging is to have varying tracer uptakes for various patients and/or anatomical regions. However, existing deep learning-based algorithms utilize a fixed model across different subjects and/or anatomical regions during inference, which could result in spurious outputs. In this work, we present a novel deep learning-based framework for the direct reconstruction of attenuation and scatter-corrected PET from non-attenuation-corrected images in the absence of structural information in the inference. To deal with inter-subject and intra-subject uptake variations in PET imaging, we propose a novel model to perform subject- and region-specific filtering through modulating the convolution kernels in accordance to the contextual coherency within the neighboring slices. This way, the context-aware convolution can guide the composition of intermediate features in favor of regressing input-conditioned and/or region-specific tracer uptakes. We also utilized a large cohort of 910 whole-body studies for training and evaluation purposes, which is more than one order of magnitude larger than previous works. In our experimental studies, qualitative assessments showed that our proposed CT-free method is capable of producing corrected PET images that accurately resemble ground truth images corrected with the aid of CT scans. For quantitative assessments, we evaluated our proposed method over 112 held-out subjects and achieved an absolute relative error of 14.30±3.88% and a relative error of -2.11%±2.73% in whole-body.