I don't know if Adobe Muse is the best tool to do this with. I don't know much about programming.
The plan: I put markers on a video made in Adobe premiere pro. People can upload these videos in Adobe Muse (via a widget?) after uploading this video opens in a video player. On the right side there is a search bar in wich you can type words with the makers put in the video via Adobe premiere. These markers then show up on the video timeline.
Is this possible? Is Muse an ideal tool for this? How do I start making this? Or does this already exist and where do I find it?
I can read HTML and understand it kind of, but I don't know how or what to write...
Downloading video files is possible.
Reading markers within a video and jump to it: No, this can't be done. Even for a hand coded site, this would be a very heavy task – if something like this is possible at all.
Markers are stream metadata. You need a server-side method (i.e. a processing app) to read them and convert it e.g. to some XML file that can be parsed and integrated into a web page. Unless you are an experienced web coder who can cite PHP and Ruby in his sleep and knows how to develop a .Net/ ASP binary executable to boot, you are way in over your head even dreaming of this. That being the case, you should rely on existing video services and make them work for you as best as you can.