A specific system architecture designed for Internet of Things (IoT) applications is serverless edge computing. It makes use of edge computing to enable code execution close to the data sources and serverless computing to reduce operational management. However, serverless function scheduling becomes more challenging due to resource-constrained edge infrastructures and highly dynamic, latencysensitive applications. Furthermore, current serverless scheduling systems frequently overlook important aspects like carbon emissions, cost, and SLO violations and prioritize only latency, model accuracy, and throughput. Therefore, in this paper, we introduce a carbon and cost-aware scheduler framework called MLPTFDDQN, which integrates a multi-layer perceptron-threshold filtering (MLP-TF) with a double deep Q network (DDQN) for adaptive function scheduling. In this framework, we first estimated each incoming function's execution time and resource requirements using an Enhanced iTransformer-based predictor. Next, a Node Compatibility Scoring and Filtering Model based on MLP-TF is used to choose a set of feasible edge nodes. Then, DDQN with a modified epsilon-decreasing strategy is used to select the suitable node-container pair to schedule the function. Experimental results on the Alibaba and Huawei datasets demonstrate that the proposed MLPTFDDQN significantly outperforms state-of-the-art baselines, achieving up to a 39.31% reduction in carbon emissions, a 37.20% reduction in total cost, and a 24.15% reduction in SLO violations.