No matter what the maximum aperture of the lens, the plane of absolute focus is the same. That is, if you shoot with a 50mm f1.4 or a 50mm f2.8 at, say, 10 feet out, it is focused on the exact same specific point of your subject. The difference is that at f1.4 a thin slice appears to be in focus and at f2.8 a thicker slice appears to be in focus.

So, let's say you are using the 50mm f1.4 lens set to f8. The resultant picture shows a thick slice of area in focus, just as a normal zoom lens set to f8 would. When you are focusing to take that photo, regardless of which lens and what focusing mode you use, you aim to focus on the exact same plane. In that regard, focusing with either lens is neither more or less difficult.

Of course, experience says that's not quite true: most will agree that focusing an f1.4 lens is more difficult than focusing an f5.6 zoom lens. The reason it's considered more difficult is because of that narrower plane of focus which shows less in focus and therefore makes it a little difficult to tell what precisely has been focused on. That's sort of a misnomer, however, because if your lens is set to f8 placing the plane of focus in exactly the correct location is irrelevant: the resulting photo will have a larger depth of field and hide any inaccuracy you had when focusing.

But, people don't buy an f1.4 lens to shoot at f8; they buy them to shoot at f1.4! If you misfocus slightly when shooting at f1.4, it won't be hidden like when shooting at f8. You do need to worry about being more precise in placing focus where you want it when shooting with such a large aperture. Is it more difficult? I think that depends upon your perspective and understanding:

• Perspective: a thin plane of focus means it's easy to see exactly what is in focus. You can tell precisely where you have focused and it's no surprise what the resulting photo looks like.
• Understanding: using a wide-area AF mode is almost asking for trouble, for example, because it's trying to focus on much of your scene, which can't be rendered entirely in-focus at f1.4. Use a single-point AF mode to place focus precisely. If using manual focus you need to have a feel for how much throw the focus ring has to recognize how much to turn it to pull your subject into focus -- just racking back and forth trying to find it will get you nowhere.

Working with an f1.4 lens isn't anything to be concerned with, IMO, because after using it for a while you'll have a good feel for it and know best how to use it.

Regarding your example photo:

Isn't the whole trunk in focus here? Why aren't some parts of trunk out of focus then?

Look close -- the whole trunk is not in focus. near the edges of it you can see it's a little soft. I bet that they could have stopped down to f1.6 or 1.8 and the edges would be a little more in focus, and the rest of the scene would basically be unchanged.