Is it possibloe to create a shading with a "comics screen tone" effect or an effect similar to the "disolve" layer effect in photoshop?
The easiest way to do this would be with a composite map layering the pattern over your diffuse colour / texture. You can do this with any kind of procedural pattern as shown in the screenshot or make your own in Photoshop. Keep in mind you'll have to do some UV Unwrapping to make it look good on your model.
If it's more a general Cartoon / Anime look you're after check out the Ink 'n' Paint shader and / or mental ray contour rendering.
And if it needs to be really specific there is other software available such as Pencil+ for example.
http://www.psoft.co.jp/en/product/pencil/
Composite Map:
With ink and paint, you can put a halftone pattern map in the Shaded map slot. That can give you a comic book like effect.
For more varied levels of halftone, like news print photos, it's probably best doing it post render, with filters or effects in a compositor, many have such effects.