Can I e-file my taxes and request for a direct deposit to a bank that is out of the states eg Singapore?

No.  The IRS will not make a direct deposit to a foreign bank.  They will only mail a check to the address on your tax return unless you have a U.S. bank account.

Oh, hmm I received a check though... But it is not approved by my local bank due to a part of my name not being imprinted on the check ..