What does a light wave look like? (3D model)

The first 2-D image you posted is a typical simplification for teaching purposes. In it, they use the height of the sine wave to represent magnitude, and the directions of the sine waves to show how the fields point relative to each other. The light itself however is not itself at all cone-like. You have to imagine this sine wave existing at multiple points in space, not localized in this cone-like volume. This can be difficult to visualize.

A common method for visualizing these kinds of fields is a 3-D vector field plot.

Length or colour will typically correspond to amplitude, and the arrows show direction of the electric field. The magnetic field is always perpendicular, and the amplitude is proportional, so there's little sense in plotting both together. This one I've included shows how the field actually permeates a volume.

Out of interest, here's a gif of dipole radiation. This is just a 2-D slice of the field, and doesn't show vector direction, but is a very good visualization of a more real-life kind of radiation. Colour corresponds to magnitude in this case.

It highly depends on wavefront shape. And wavefront depends on the source. If your source is a star and you are far from it and detect the wave, the wavefront is planar There are many another wavefront shape for a different source. These are only the most common