First, the town where Albert Heinrich was born is correctly spelled Staffhorst.Staffhorst was not in Prussia.Staffhorst was in Hanover.Staffhorst is about 10 miles from Hoya.
The town where Albert Heinrich died is correctly spelled Bücken, not Bucken, and the nearby town is Warpe, not Warne.
Albert Heinrich's wife's correct name was Gesche Margaretha.(Gesche is short for Gertrude.)Their second son's correct first name was Friedrich.Your direct ancestor's correct name was Johann Friedrich.Albert and Gesche's daughter's correct name was Sophie Maria.Her husband's correct first name was Diedrich.
There was no "Hanover province".Until 1814, Hanover was an Electorate, and then in 1814, it became a Kingdom.In 1866, the Kingdom of Prussia annexed the Kingdom of Hanover, which THEN became the Prussian province of Hanover, which it remained until 1945.Its capital was the city of Hanover.(As you may know, Hanover was in personal union with Britain from 1714 to 1837, the King of England during those years having also been Elector, from 1814, King of Hanover.)
Following World War II and the break-up of the huge state of Prussia, the Prussian province of Hanover, the state of Oldenburg, and the two very small states of Brunswick (in German: Braunschweig) and Schaumburg-Lippe combined to form today's state of Lower Saxony(in German:Niedersachsen), the capital of which is the city of Hanover.
There is no such place as "Longleid", and I really can't imagine what that could actually be.
And because there was no unified Germany until 1871, you could leave "Germany" off of the places you list.It makes no difference.