Hi combitz,
Constraints on derived fact types are themselves derivable and can be shown on the diagram. Thus, in your example, if the Person role in "Person has DOB" is required, and assuming the age calculation is derived from that date and the current date (which is known), then the Person role in "Person is of Age" would be mandatory as well. However, if the Person role in "Person has DOB" is optional, then the Person role in "Person is of Age" must also be optional. Uniqueness constraints are derived in a similar fashion so assuming a Person can only have one DOB, the uniqueness constraint must span only the Person role in "Person is of Age" (i.e. a person can have only one age).
There is no construct for multi-valued attributes in ORM as cardinality is handled by the internal uniqueness constraints on fact types. Thus, if you had some sort of multi-valued ER attribute such as a collection of colors for a car, you would model this as the fact type "Car is of Color" and have the uniqueness constraint span both roles. Entity naming is handled by the tool. For example, in NORMA, you can name the fact type and that name would be used to derive the table name. In other ORM tools, you can force the table name on mapping via objectifying the fact type as the objectified name would then be used for table naming (a bit clumsy, but it works).
For composite types, the most common approach is to use co-referencing.
http://www.objectrolemodeling.com/WebLog/tabid/58/EntryId/33/Default.aspx covers this a little bit but basically, you would create an object type representing the composite type and then have the composite’s detail modeled as fact types (e.g. Person Name has First Name, Person Name has Last Name, etc.). You then make the composite role unique on each fact type and place a external uniqueness constraint on each component role. Then you are free to use the composite object type and all component roles are then absorbed. Note, however, that your table mapping may be a little off depending on the tool you use and whether or not all component roles are mandatory. As for display on the diagram, most tools only require you to have the component fact types displayed once but allow you to repeat them for each use of the composite if desired.
Hope that helps,
Scot.