Can a CK have a FK referencing to a CK in another table?
Department (Dept, Dept_name)
Employee(RegNo, FirstName, LastName, BirthDate, Dept_fk, Salary, City)
Dept_name is a CK of the Department table.
Can Dept_fk be part of a CK (Dept_fk, FirstName, LastName, Birthdate) in Employee when Dept_name is not set as primary key in Department table?
Two definitions of "CK (candidate key) of a given table" are:
We cannot determine the CKs of a table without the information needed by the definition we are using. Eg all the FDs (functional dependencies), or a canonical cover of FDs or all the column sets whose subrow values are unique, etc. That information can always be expressed without involving another table.
We can pick one CK of a table to call "the" PK (primary key) of it. PKs are irrelevant in relational theory. (If you are using an ER method and it has rules about PKs vs CKs then you should reference & tag it.)
Dept cannot be part of candidate key (ex.: Dept, FirstName, LastName, Birthdate) in Employee table since Dept is not set as primary key in Department table
Dept is not in Employee so it can't be part of a CK of it. But if you added it, whether it was a CK of it is independent of other tables.
If you are asking about whether you can do something based on a distinction between Dept being a CK vs PK in Department: PKs are are always irrelevant.
If the "Dept"s are typos for "Dept#": The mere fact that Dept# is or is not a PK of the Department table has no bearing on the CKs of another table. Whether it is a PK vs CK is always irrelevant.
But can I still call Dept a candidate key just knowing that Dept is a candidate key in the Department table?
It's the CK of Department. So in English we can say that it's a CK. But to be a CK is to be a CK of a particular table.
Maybe you mean "can I still call Dept a CK" of Employee just knowing...". Only if you show that it is one. And whether it is one is independent of any other table.
(Maybe you should be calling some things FKs in this question?)
PS A column can appear in multiple tables without a FK between them. ("Reference" is only useful when you are talking about a FK.) Different columns can have FKs between them. There is a FK if and only if all subrow values in one set of columns appear in another ("referenced") one. An SQL FK only has to go to a superkey (superset of a CK) not a CK. A FK can be from any column set: a FK is only a (super)key in the referenced table. Learn the definitions of FD, superkey, CK, PK, FK (to CK or superkey).