Domain - Specifies the technical attributes of a data element that are its data type, length, possible values, and appearance on the screen. Each data element has an underlying domain. A single domain can be the basis for several data elements. Domains are objects in the ABAP Dictionary.
Data Element - Specifies the business function of a table field and its technical attributes are based on a domain. Its business function is described by its field labels and documentation.
Aggregate Object – Views, Match Code and Lock objects are called aggregate objects because they are formed from several related table.

Yes

A data element describes the role played by a domain in a technical context. A data element contains semantic information.

Yes. We can assign a domain to data element by just overwriting the entry in the field domain.

No.

Yes. There is no domain for a field if we want to specify no data element. We can enter data type and field length and a short text directly in the table maintenance.

No, we cannot delete data element that is being used by table fields.
No, when we try to do so, it throws an error.