"A week is a sprint", I think it is to short because of the overhead you gain with Planning, Retro and Review.
"developer and designer achieve at least one goal by the end of Friday" I hardly believe tasks and/or stories can be exactly planned like this, a task with lasts exactly one week suited for the experience of the dev is hardly planable. Also a team commits to the Stories and Features not a single team member, be it a dev or designer
"The one responsible for this task is also appointed to update our weekly change log and schedule board. A single entity/manager comparing the planned schedule with actual development for 6 months is therefore discouraged" We had various ProductOwner in the beginning, it didn't work out, here I think the principle "Design is not a democracy" applies. Let one keep track of it.
"Stories should be prioritized and categorized by their importance and estimated development time" hardly possible because of dependencies. I know some Scrumdefenitions say that Tasks and Stories should be independent but in reality they just aren't.
One more tip, don't forget the review and retro and to put the outcome in the feedbackloop.