Como se dice trabajo a destajo en inglés

Piecework.

Piecework: work for which the amount of pay depends on the number of things finished rather than the time spent making them.
Cambridge Dictionary Online.

Piecework:  work in which you are paid for each thing you make or do and not for the amount of time you work
Merriam Webster Dictionary.

Tener sello húmedo (un documento)

To get/have the rubber-stamp.

"Your application should get the rubber stamp from the residents' association."
Oxford Advanced Dictionary.