Pyramid
The description given seems to fit that of a square based pyramid.
I AM A SPACE FIGURE WITH 5 FACES, 8 EDGES, AND 4 CORNERS. which SPACE FIGURE AM i?
A four faced figure is a tetrahedron. If they are all congruent triangles, they are all equilateral triangles and it is a regular tetrahedron - one of the 5 Platonic Solids.
yes
A rectangular pyramid has 5 faces: a rectangular base, and 4 triangular faces.
pyramid
pyrmid
Assuming that a space figure means a 3-dimensional object, the answer is a square based pyramid.
rectangular pyramid
square
Nothing
This is an impossible three-dimensional figure. A pyramid has 5 faces and 8 edges but has 5 corners, not 4. A 4-cornered three-dimensional figure has only one itteration: that of a 4 sided pyramid of 6 edges. Since your shape is 5 sided with 8 edges I would say you have got a number wrong there somewhere.