Yes. Think of a glider, and then imagine folding its wings in half.
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Surface area is ONE thing that can affect how fast an object falls. Two forces determine how fast an object falls - the force of gravity and the opposing drag on the object from the medium it is falling through. In the case of an object falling in a vacuum, there is no drag so the object falls strictly according to the law of gravity. If an object is dropped through a fluid such as air or water, it can reach a terminal velocity where the force of gravity is exactly counterbalanced by the opposing drag on the object. In this case acceleration ceases - although motion does not. In other words, the object continues to fall, but it doesn't speed up. Drag force is a function of object velocity, viscosity of the fluid it is falling through, the surface area of the falling object, the surface roughness of the falling object, and the geometry of the falling object (spheres usually have less drag than cubes for example).
It depends on the object!
If the surface is sticky the energy needed to break the "sticky" ionic bonds will not be able to contribute to the motion of the object rolling down the inclined surface.
Mass does not directly affect surface area. Surface area is a measure of the total area of an object's external surfaces, while mass is a measure of the amount of matter in an object. However, as the mass of an object increases, its volume typically increases as well, which can indirectly affect its surface area if the shape remains constant. Objects with larger masses may have larger surface areas if their volume increases proportionally.
The terminal velocity of a falling object depends upon its aerodynamics (which is to say, its shape) rather than its size and mass.