where does the water come from that flows over niagra falls?

Its a complicated process

The water actually starts in the Atlantic Ocean (Gulf of Mexico), from there it flows up the Mississippi River into Lake Superior (Minnesota side). Lake Superior then flows into Lake Huron via the St Mary' river, and then down to Lake Michigcan, it then flows through Lake St Clair. The water flows through Lake St Clair into Lake Erie, where it flows north, and ends up flowing over the Niagara Falls.

Surely you were taught the water cycle at school.

It comes from Lake Erie.

The sky.  It falls as rain or snow.

Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and all their tributaries.

Niagara Falls...It comes from Lake Erie via the Niagara River

It’s a closed system. Massive pumps at the bottom send the water back to the top.

Niagra river flows from the Great lakes 

The Great Lakes