This requires a couple of different solutions, however I’ve done something similar.
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To replace the logo and other UI elements, you’ll have to modify the template files and provide a path to your custom templates using a custom configuration snippet in TLJH. Templates use Jinja, which is basically HTML with some dynamic elements.
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I assume you’re referring to the menus within Jupyter Lab or Notebook. To modify these, you’ll have to modify the Lab or Notebook configuration. This is trickier and I don’t have an exact answer.
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To make a cell readonly, you can set
"trusted": true,
"deletable": false,
"editable": false,
in the cell metadata. Then, you’ll have to set showEditorForReadOnlyMarkdown: false in the Advanced Settings. Unfortunately, I don’t know how to set Advanced Settings options for all users. I’m currently trying to figure this out as well.
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If by “embed a plain notebook” you mean providing a default notebook, this can be done with nbgitpuller.
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You can change the font for the web pages by editing the template and providing custom CSS files. Not totally sure how to change the font for Jupyter Lab/Notebook.
Finally, if you are primarily trying to create a simple interactive tutorial, Jupyter Book may be a better option. It lets you easily create and deploy notebooks, which can even be executable.