It is my first question: What pieces of software do I need to create a website that is going to copy my YouTube Channel? All I need are: 1) Ability to add videos (thumbnails are here, videos are on YouTube), 2) Ability to add comments for every video?
Do you want to embed each YouTube video separately? You can do that on any website you build (e.g. HTML5, WordPress, Drupal, etc.)
Do you want to upload the videos directly to your website? You can upload videos to your server.
Do you want a website that mimics YouTube. You can install ClipBucket or CumulusClips via Softaculous but neither has been updated in over 2 years.