1) I would still keep it in the category table... its ok if those are blank for subcategories.
2) Usability decisions can be made by you... If that is what you think is best for the client, then keep that approach.
3) Again this is a usability decision... Multiselect lists, repeating lists, checkboxes would all be acceptable
The decisions you make on the admin really depend on what you think the most common use case is based on the application and what your client is comfortable with and what type of device they might be using.