For accessibility reasons, using the latin alphabet is recommended (specially for categories because redirections don't work). For museums whose official name doesn't match, the most current “latinized” name should be used instead. This will generally be the English translation, as found on the English Wikipedia, but the situation must be evaluated for each case.
Categories are the most convenient way to manage the whole collection of a museum.
As there are many different situations depending on the museum type/size/policy, it is not possible to provide a global unique solution for museum categorization. Nevertheless, general schemes are the same everywhere, and upper categories should be in form of:
Subcategories of “Building” and “Temporary exhibitions” are then easy to imagine
The point concentrating the main problems is the substructure of “Permanent collections”. The experience showed that multiple approaches were possible and mutually beneficial, mainly by room and by type of work:
Of course, this example will have to be adapted for very big museums, where the collections are divided by departments; and for the most little ones also, where too much categories could be harmful. But in most cases, it should be fine.
Too many images on Commons are unusable because they are uploaded without sufficient description.
However, providing relevant informations on photos taken in museums is generally painless because these informations are often indicated in the museum caption (tip: always shoot it after the object itself). Notable among them are: