The scope of the International Workshop on Spoken Language Translation (IWSLT) has recently broadened beyond traditional Speech Translation (ST) to encompass a wider array of tasks, including Speech Question Answering and Summarization. This shift is partly driven by the growing capabilities of modern systems, particularly with the success of Large Language Models (LLMs). In this paper, we present the Karlsruhe Institute of Technology's submissions for the Offline ST and Instruction Following (IF) tracks, where we leverage LLMs to enhance performance across all tasks. For the Offline ST track, we propose a pipeline that employs multiple automatic speech recognition systems, whose outputs are fused using an LLM with document-level context. This is followed by a two-step translation process, incorporating additional refinement step to improve translation quality. For the IF track, we develop an end-to-end model that integrates a speech encoder with an LLM to perform a wide range of instruction-following tasks. We complement it with a final document-level refinement stage to further enhance output quality by using contextual information.