Does the external auditor report on whether the published financial statements are correct or not?

The auditor provides a reasonable assurance that the reported financial statements are free of material misstatement. Therefore, the auditor is responsible to only to search for significant misstatements, not minor misstatements that don't affect users' decision. In addition, by using term reasonable assurance is intended to indicates that an audit cannot completely eliminate the possibility that material misstatements will exit in the financial statements.

Yes auditor reports claims that it is inline with Accounting standards, company following rules and regulation of the country, there is no any false statement, the figures are true, this report help the investors whether they should invest or not in that company.