Is there a way to pass to execute immediate only once a variable but use it several times?
I don't know of any built-in way to accomplish this but you could use a derived table or a Common Table Expression (CTE or as Oracle likes to call them: subquery_factoring_clause), if your aim is to pass the parameters only once in the USING:

-- derived table
OPEN myCursor FOR
    SELECT value1 AS Value1,
      myPackage.function1 (value1, my.id) AS Result1,
      myPackage.function2 (value1, my.id) AS Result2,
      myPackage.function3 (value1, my.id) AS Result3                       
    FROM (SELECT :myId AS id, :myPk AS pk FROM dual) my 
      CROSS JOIN 
        mySchema.myTable
    WHERE tpk = my.pk
USING myPk, myId

-- CTE
OPEN myCursor FOR
    WITH my AS
        (SELECT :myId AS id, :myPk AS pk FROM dual)
    SELECT value1 AS Value1,
      myPackage.function1 (value1, my.id) AS Result1,
      myPackage.function2 (value1, my.id) AS Result2,
      myPackage.function3 (value1, my.id) AS Result3                       
    FROM my 
      CROSS JOIN
        mySchema.myTable
    WHERE tpk = my.pk
USING myPk, myId