Briefly:
(i) looks like a hyperboloid, but there is an extraneous z term. This implies that when viewed along the z axis, we have an off-centre hyperbola (x^2 and y^2 terms with a displacement of the centre) as a cross-section. This cross-section has varying parameters depending on z.
(ii) is an ellipse or a cylindrical ellipse (fixed cross-section).
(iii) is an ellipsoid.
(iv) is neither an ellipsoid nor a hyperboloid.
I hope this is meaningful.