I want to know if autofocus is important for ultra wide angle lenses, for casual users. I mean, users like my mom. I don't mind about manual focusing, but I suspect that wide angle lenses will focus the entire scene without need to focus, but I want to be sure about this.
It really depends on the skill level of your mum. If she has a basic idea then it wouldn't matter. However if its for point and shoot photography, and she will want to photography a wide range of subjects, then autofocus might be more appropriate.
Critically, the depth of focus will be wider at any given aperture, so if the lens was left at say, f8 then she would likely be fine. If however she were shooting wide open and had objects both very close to the lens and in the distance that she wanted in focus, then she will struggle. If your mum is the type to not understand or even touch an aperture, then I would suggest autofocus would be easier.
I will also add that the lens choice should depend more on subject choice than technical ability. If your mum wants to shoot portraits, unless her name is Bill(ie) Brandt, she likely won't be happy with an ultra wide.
For the record, I wouldn't personally shoot with an autofocus lens. But then I have specific needs and understand them and how the camera helps to achieve them. If you are learning, it is often easier to start with a camera and lens that offers as much automation as possible but allows you to override it, so that you can gradually learn what is important in your own work.
In a word, No. As you guess, focus is much less critical with a very wide angle lens. First, the depth of field is inherently much better than with telephoto lenses. As a journalist, I relied on a 24mm wide angle (35mm standard film body) for a lot of fast moving indoor shots. Less demanding than longer lenses in terms of light needed, motion blur, shake, focus, and even distance/room required to shoot in.
My wide angle lens's focus goes slightly beyond infinity (it's the same for most other lenses too). If I turn the focus ring all the way, as far as possible, the picture will not be as sharp as a properly focused one, even at 12 mm zoom (APS-C) and f/10. So the whole scene will not be "automatically" in focus, regardless of how the focus ring is turned.
Manual focusing does require some skill and good vision, especially in a small viewfinder. If the user doesn't have good vision or is not willing to put in the effort to carefully examine if the scene is in focus, then it probably won't be a good experience using such a lens.
It is definitely true that accurate focus is less critical with a wide angle lens than a telephoto. But a wide angle lens does not eliminate the need to focus, at least not unless you somehow manage to lock it at infinity focus and then only shoot things that are far enough (which is not that far with a wide angle).