Term describing the practice of anticipating dangers while driving

You might consider foresight (vorausschauend is translated by Google as "foresighted").

foresight [mass noun]
the ability to predict what will happen or be needed in the future:
he had the foresight to check that his escape route was clear

but anticipating any hazards by close observation (such as being ready for the child playing near the road to chase his football) can indeed be called anticipatory driving. Different terms may be used in different countries.

To anticipate, is to take action when you expect something will or might happen. The way you anticipate what might happen is to make early use of all the information available to you. To do this effectively you need to be constantly aware of what is happening around you. You should constantly be scanning the road ahead and checking your mirrors. Take in as much information as you can. Be aware of what is happening:

ahead
behind
to the side

Keep your eyes moving. Pay attention to the middle and far distance, not just what is happening immediately ahead of you. Try and see the bigger picture, don't allow your eyes to be drawn to just one area. Looking further ahead will enable you to see things earlier and give you more time to deal with them.

http://www.driving-test-success.com/anticipationandplanning.htm

In the US, the most common term is defensive driving

The standard Safe Practices for Motor Vehicle Operations, ANSI/ASSE Z15.1, defines defensive driving as "driving to save lives, time, and money, in spite of the conditions around you and the actions of others."

It is a form of training for motor vehicle drivers that goes beyond mastery of the rules of the road and the basic mechanics of driving. Its aim is to reduce the risk of collision by anticipating dangerous situations, despite adverse conditions or the mistakes of others.

There is a term, "defensive driving" which encompasses what you mention.

Defensive driving is a form of training for motor vehicle drivers that goes beyond mastery of the rules of the road and the basic mechanics of driving. Its aim is to reduce the risk of collision by anticipating dangerous situations, despite adverse conditions or the mistakes of others. This can be achieved through adherence to a variety of general rules, as well as the practice of specific driving techniques. — Wikipedia

(Would just have left this as a comment, but don't have the reputation.)

In the UK, as well as practical and theory tests, to get a driving licence you have to pass a "hazard perception" test involving watching a video of someone driving, and clicking a mouse when you see a developing hazard. ("A developing hazard is something that may result in you having to take some action, such as changing speed or direction.”) This sounds similar-ish to what you're after.