Could a cohen (or any israel I suppose) marry a Jewish woman whose parents had a civil wedding? (not religious, meaning without ketouba) what would be the way to follow in this case? (which steps would an orthodox authority require to proceed with this union? ask the parents to get a ketouba?) Thanks

A Ketuba is not the only condition for having a proper Jewish wedding according to Halacha. A Rabbi must know the full details to determine if this marriage is halachicaly binding and what has to be done if they want to get or remain married in a religious fashion. Consequently, the child may be viewed as being born out of wedlock and this has further consequences in regard to a cohen. As said, all details must be given to the officiating Rabbi to give a proper comprehensive answer.