Just ordinary perspective, 2 point, using slightly curved lines for effect instead of straight lines.
and yes to do a good perspective you need to draw in the horizon and pick your vanishing points, sometimes these are off canvas so your canvas in the drawing phase can often be bigger than the picture you intend to draw so you can get your perspective lines right.
Those all look like completely ordinary rectilinear perspective/gnomonic projection, or pretty close to it. They are just close up with wide angles, but no fancy non-linear projections. You'd draw it the same way you'd draw any normal perspective image.