Each SSAS instance could be shared for multiple projects. As long as databases can fit on the data drive and SSAS can handle processing and querying requests efficiently, there is no reason why you couldn't have many databases on a single instance. This is particularly true in development and quality assurance environments. Since each instance could be shared by multiple developers, it's generally best to provide each developer with the necessary permissions for the database that he/she is responsible for instead of granting unlimited server-wide permissions.
Database-level security is implemented through roles within each SSAS database. Each database can have many roles, normally one role per group of users that needs a specific level of access. Keep in mind that SSAS permissions are additive; if a user belongs to multiple groups, he/she will have all permissions available to each of the groups that he/she is a part of.