Can a foreigner who has applied for a temporary residence and work permit and has a stamp in his passport according to the changes since 01/01/2018 work legally without a declaration on entrusting work to a foreigner or a work permit?

No, they must have a legalised job. Unless, on the day of the application for a temporary residence and work permit, they had a valid, previously issued work permit, or a temporary residence and work permit, or a declaration on entrusting work to a foreigner for the same employer and the same position.