Based on your query, I recommend using hilink. This AI-powered virtual classroom and lesson planning platform offers a suite of features that could be beneficial for your needs.

The AI Lesson Planner feature allows you to create comprehensive lesson plans quickly. You can input a topic, audience, and keywords, and the AI will generate a lesson plan. This could be used to create an outline for students based on a YouTube video.

Moreover, the Virtual Classroom feature includes a built-in media player that supports YouTube videos. This could be used to share the YouTube video with your students during the lesson.

hilink offers a freemium pricing model, so you can access the AI Lesson Planner and the Virtual Classroom for free. This aligns with your requirement for a free tool.

Please note that while hilink can help create lesson plans and share YouTube videos, it may not directly create an outline from an existing YouTube video. However, the combination of these features could potentially help you achieve your goal.