Glad you are trying us out! I will do my best to address your questions.
if the API is an Entity, and mobile app is an application, how roles will be designated to users for the APIs? How do we access them there? Is it done via same approach as in Auth0?
Are you saying that you are looking to have the same roles (they are called permissions the entity types) assigned to an entity and a user? I may need a little more context to better understand. Maybe you could outline how you are expecting this to work in practice.
Side note, we have documentation on this to be found here (you may have already reviewed it).
https://site-local.fusionauth.io/docs/v1/tech/core-concepts/entity-management/
https://site-local.fusionauth.io/docs/v1/tech/apis/entity-management/#undefined
Also there is a question about using Roles by tenants - as we plan to create those roles, while Tenants will be assigning them to their users, is that actually possible?
Roles are scoped to an application per documentation. I might need some additional clarification/context to better address.
https://site-local.fusionauth.io/docs/v1/tech/core-concepts/roles/#overview
Let us know. Happy to help as able!
Thanks,
Josh