Data Validation

Is ‘sql injection’ already a part of that function or do I need to add my own code?

When inserting input to the database you should use prepare method of WPDB class which supports both a sprintf() – like and vsprintf() -like syntax. read more at the codex

Are there wordpress form input validation functions that I can use on my custom form?

Yes there are many and they are covered in Data Validation codex entry like toscho pointed out.

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)