Is it permissible to design and sell notebooks that might be used on Fridays or for forbidden purposes such as writing music, knowing that the majority of buyers are non-Muslims?

There is no impediment to designing notebooks and selling them to Muslims and others, even if they are used for impermissible purposes, because their predominant use is for permissible ones. There is no harm in using them on Friday, for working on this day is not forbidden except for what distracts one from hastening to the prayer. If a violation occurs on the part of the buyer, he bears the burden of its sin, and this does not constitute aiding in the forbidden.