All four words describe surfaces without significant curves or bumps, but they differ in scope. 'Flat' is the most general — a flat surface can be horizontal or vertical (a flat wall). 'Level' specifically means horizontal and even; you cannot have a level wall. 'Even' focuses on smoothness without irregularities and allows gentle slopes (an even lawn). 'Flat-topped' is the narrowest: it only describes the upper part of something. A kitchen counter is flat, not flat-topped (its top IS its whole surface); a mesa is flat-topped, not just flat (the description points to the summit specifically). Use 'flat-topped' when the shape of the crown or summit matters.
Combination of 'flat' (from Old English 'flet', meaning level or smooth) and 'topped' (from 'top', from Old English 'topp', meaning the highest part). The compound has been used since at least the 18th century to describe landforms and later other objects with a flat upper surface.