a cone
Hemisphere
Technically, there's no shape with no surface and no vertices, but a sphere is close. It has no vertices but has just one surface.
Cone
An ovoid (egg-shape) is one possible answer. A smooth blob (to use a very technical term!) is another.
cylinder
a sphere has 0 flat serfaces 0 vertices
A shape with 0 vertices and 2 flat surfaces is a cylinder. The two flat surfaces are the circular bases at the top and bottom, while the curved surface connecting them does not count as a flat surface. Other than the cylinder, a shape that fits this description is a circular disk, which also has no vertices and one flat surface, but when considering the top and bottom of the cylinder, it effectively has two flat surfaces.
Hemisphere
How about globe or a sphere
Technically, there's no shape with no surface and no vertices, but a sphere is close. It has no vertices but has just one surface.
A sphere is a solid figure that has 0 flat surfaces and 0 vertices. It is perfectly round and smooth, with every point on its surface equidistant from its center. Unlike polyhedra, which have flat faces and vertices, a sphere has a continuous curved surface.
Cone
A solid figure with 2 flat surfaces and 0 vertices is a cylinder. A cylinder has two circular flat surfaces, known as bases, and no vertices because it does not have any corners or points where edges meet. It is a three-dimensional shape that is formed by a curved surface connecting the two bases.
A blob, an ellipsoid, a torus (doughnut), a sphere
The solid figure that has 2 flat surfaces and 0 vertices is a cylinder. A cylinder consists of two parallel circular bases (the flat surfaces) connected by a curved surface. The bases do not have any vertices, as they are continuous curves.
Circle
Prism