retrieving both class permission for both see this class and can attach object to a class

The information is available via the ACL on the ObjectClass instance: M-Files API - ObjectClass Object

This ACL class is rather flexible and I don't 100% recall exactly how the properties map to the items you see on the screen there (this class is also used to represent object ACLs, for example, too), but I am pretty sure that property has the information.