The solid you are describing is called a cylinder. It has two circular faces, one curved face, and no vertices.
A frustum of a cone.
Assuming that a solid triangle is a tetrahedron, the answer is: faces: 4 edges: 6 vertices: 4
a pyramid
The solid figure that has the same number of faces and vertices and has 8 edges is a cube. A cube has 6 faces, 8 vertices, and 12 edges, so it fits the description given.
It has 6 faces, 12 edges and 8 vertices
cylinder
A face, of a solid object, is a flat surface. If it is curved it is called a curved surface though sometimes it is also referred to as a face. Two faces meet at an edge, which is a line which may be straight or curved. Three or more faces meet at a point which is a vertex.
A sphere has no flat face and no vertices. It does have a curved surface; so it depends upon your definition of a face.
Assuming that a solid triangle is a tetrahedron, the answer is: faces: 4 edges: 6 vertices: 4
a sphere
A cube is a solid figure with eight vertices and all faces of equal size.
A rectangular pyramid (four-sided base) has 5 faces and 5 vertices.
a pyramid
The solid figure that has the same number of faces and vertices and has 8 edges is a cube. A cube has 6 faces, 8 vertices, and 12 edges, so it fits the description given.
It has 6 faces, 12 edges and 8 vertices
Tetrahedron: 4 equilateral triangle faces and 4 vertices.
sphere
There is no such polyhedron.