In general: as Jay Carr visualized with his interactive graphic, velocities (speeds) are vectors (this is rather physics than aviatic, but if pilots consider physics they tend to live longer). Vectores have a value and a direction. So you can visualizes them by an arrow (lenght visualizes the velocity). Contrary to e.g. temperature which is a scalar measure, it has only a value but no direction.
So to add speeds you must consider values and directions.
Now to your questions ...
ad Image 1)
The wind is blowing from the left. If the aircraft would aim to the north ("heading north"), the cross wind would move it to the right, so it would pass the city more to its right (if map is oriented "north up" than it would pass the city east).
BUT, the pilot is smart: he compensates for the crosswind by pointing the aircraft's nose slightly "into the wind" (look, where the aircraft's noise is pointing to). Durign his flight planning he might have calculated the "offset" comparing desired track and forecasted wind. Once in the air he could also find out by applying a heading into the wind and check whether the aircraft moves along the desired track.
ad image 2)
the plane is sliding (well, it does not touch the ground) because its air speed (caused by the propulsion of the prop and being straight - visualized in the image by the wake vortices and its wing tips ) points to its noise (the prop is mounted without pivot), plus (plus in a sense of vector addition) the wind from the left result here in a track following the railways.
ad image 3)
the wind from the left moves the whole air which surrounds the aircraft (a static wind, no gusts). So the while the aircraft moves through this air mass, the air mass itself (and with it the aircraft) moves along the wind direction. So you do not need rudder to hold that direction (heading). You only have to apply rudder to change the direction. So the pilot did apply rudder for some seconds when he noted that he needs to compensate for the crosswind, just until the aircraft changed its direction from north to slighly north-north-west.
The author says "the aircraft does note feel the crosswind" - yeah, due to its static effect you could not tell without any reference (to the ground, to your GPS or whatever navigation aid) that there is a wind at all.
To bring Wurzel's answer into the context: yes, if you want to land then you could use the same maneuver as shown in the 3 images (called crab, because this animal walks sideways), - or if you could fly straight along the runway direction but compensate for the crosswind by lowering the windward wing.
Hope it helps