color mapping

You can use a vector effect for color mapping (in the Effects menu, first section).

I will test what happens with the image export to EPS.

In VS (ok):

In AD:

Is it possible not to have all these lines, as the result could even be of better quality than obtained with AdI?

The only way to not have those lines is to turn off anti-aliasing with View -> Subpixel -> None.
Same when exporting to images, the anti-aliasing can be turned off in the export settings.

This is a rendering artifact from the type of anti-aliasing algorithm used in VS (similar thing happens in Affinity also).

@Pat The lines are caused by anti-alliasing of touching shapes.

Is it possible not to have all these lines, as the result could even be of better quality than obtained with AdI?
There are also many options with combinations that are impossible to test all in a workflow with limited time.

Original/VS/AI:

VS doesn't trace although it seems so

That is true. In that case the trace button should be grayed. I will fix this.

@Pat Got the file. The image was not yet traced (it also looks too smooth to be traced in the screenshot).

Agree but when "Extract something" is unchecked, VS doesn't trace although it seems so...

@Pat The resulting objects will be clipped into a rectangle (the original image frame), but that should not have a fill.

: you must do an "Expand" on the trace first.

@VectorStyler I can expand when the quality of the tracing is not high & I can not when it is ok:

So far, I have to trace png files in AdIllustrator to get what I need & I import in VS.

An "Object -> Shape -> Clear Object Shape" should remove the clipping from the traced group. BTW: you must do an "Expand" on the trace first.