I have no idea how to import a mesh into unreal

The pivot point for each object in Blender is the small dot displayed at its center.
What you think is the object’s pivot is not the object’s bound pivot, but the position of a temporary pivot. By default, it is set to the median point of the selected object.
You can move the 3D cursors using Shift+S and change the object’s pivot to the 3D cursor’s position via the Object menu.