Recent advances in dermatological image analysis have been driven by large-scale annotated datasets; however, most existing benchmarks focus on dermatoscopic images and lack patient-authored queries and clinical context, limiting their applicability to patient-centered care. To address this gap, we introduce DermaVQA-DAS, an extension of the DermaVQA dataset that supports two complementary tasks: closed-ended question answering (QA) and dermatological lesion segmentation. Central to this work is the Dermatology Assessment Schema (DAS), a novel expert-developed framework that systematically captures clinically meaningful dermatological features in a structured and standardized form. DAS comprises 36 high-level and 27 fine-grained assessment questions, with multiple-choice options in English and Chinese. Leveraging DAS, we provide expert-annotated datasets for both closed QA and segmentation and benchmark state-of-the-art multimodal models. For segmentation, we evaluate multiple prompting strategies and show that prompt design impacts performance: the default prompt achieves the best results under Mean-of-Max and Mean-of-Mean evaluation aggregation schemes, while an augmented prompt incorporating both patient query title and content yields the highest performance under majority-vote-based microscore evaluation, achieving a Jaccard index of 0.395 and a Dice score of 0.566 with BiomedParse. For closed-ended QA, overall performance is strong across models, with average accuracies ranging from 0.729 to 0.798; o3 achieves the best overall accuracy (0.798), closely followed by GPT-4.1 (0.796), while Gemini-1.5-Pro shows competitive performance within the Gemini family (0.783). We publicly release DermaVQA-DAS, the DAS schema, and evaluation protocols to support and accelerate future research in patient-centered dermatological vision-language modeling (https://osf.io/72rp3).