Hi 
1) Yes, only if you are e.g. Owner of Schema, then you can Manage Grant of this schema and underlying tabes to others
Please check his docs:
https://docs.databricks.com/en/data-governance/unity-catalog/manage-privileges/ownership.html#owners...

2) Regarding mounts:
I don't think this is possible to restric command itself, if our users will come with valid e.g. Access Key and Storage Account - they will be able to mount the Storage.

I am not sure about below statment but you can check it by yourself:
I think with Unity Catalog enabled cluster with SHARED access mode you won't be able to use or create mounts. If this is correct just grant access to Shared cluster for your end users but please check it before.
Please remember that mounting is not recommended way now as we have External Locations in Unity Catalog