Is it possible for multiple sites to each set up database of their own? In addition to that, will those multiple sites be able to access the same user roles and information?
Database is important of a website. This is where all data are stored such as images, pictures, videos, text and other file extensions use to design a website.
Multiple website uses there own server and database, this is needed to protect there own websites's database. A database that consist of files, pictures, texts, videos and the content of there website.
Some has multiple websites in different locations to localized the features and storage. They just have to inter-connect database that allows them to access the file from other database use for sharing data information.
There are advantages and disadvantages of using multiple database and single but Macro-database. For multiple database used, it protect the database in one location. It safeguard the specific file in the local region compare to Macro-databased that use single storage in all locations. If the database encounter failure, then it'll be mess all out because it doesn't have back-file or source.
 Yes off course you can. Your website implementation is depending on your design or set-up. You can set-up multiple websites in just one database as well as multiple websites having individual database. What you need is just to implement access to a particular database for the website.
A centralize user access can be also set on your own implementation. If you have notice nowadays, that there is sharing of user accounts like what the Google are doing. Same thing with FaceBook accounts. You can see that there are some sites allowing Google accounts to access their website, this is by means of API. You can do this also using your own API. What you need is the design and the implementation.
