Is there a Sunnah or a reported supplication, or a two-rak'ah prayer, or the offering of dates and milk upon the opening of a commercial shop?

The prophetic guidance for such an activity is to perform Istikhara (prayer for guidance), based on the narration of Jabir (may Allah be pleased with him), who said: "The Prophet, peace and blessings be upon him, used to teach us Istikhara for all matters."

As for offering dates, milk, and the like, there is nothing authentically reported about this. However, there is no harm in offering them on such an occasion as a custom, not as an act of worship. This means there should be no belief that this has any effect on the blessing or growth of the place.