SQL Functions - PostgreSQL

Hi guys.

I have some questions about SQL functions in postgresql:

1. Can a SQL function call another SQL function?

2. How about recursive calls?

3. Consider we have function that has a varchar argument.

   CREATE FUNCTION func(varchar) RETURN void AS $$
   some SQL queries.
   $$ LANGUAGE SQL;

Should we define the argument, varchar or we should define the length too like varchar(20)? How about return values?
4. consider this example:
we have table named student and a function like this: it only gets a student row and add that row to the student table.

CREATE FUNCTION add_new(student) RETURNS void AS $$
INSERT INTO student VALUES ($1);
$$ LANGUAGE SQL;

is this function syntactically right?

Thank you very much.