Why don't you just create a Stored Procedure in the DB and add it to Entity Framework, or call it via ADO?
I'll even give you the SP code
INSERT db2.dbo.NEWSTD (ID, NAME, BRANCHCODE, COUNTRYCODE)
SELECT ID, NAME, BRANCHCODE, COUNTRYCODE, 0
WHERE ID NOT IN (SELECT ID FROM db1.dbo.STUDENT1)
The last line which is commented out will prevent duplicates if you un-comment it