how to translate expressions involving "of" into German

Question

I am conducting a research to find a way how to translate the English expression "of XXX" into German.

A have found that there are three different options to express it (sometimes only some, sometimes all can be used).

1. a compound noun
2. "von"
3. genitive case

Let's consider these 5 sentences (numbered 1 to 5) and their 3 options:

1. "the color of the car"

   • die Autofarbe
   • die Farbe von dem Auto (die Farbe vom Auto)
   • die Farbe des Autos

2. "the photo of the car"

   • das Autofoto
   • das Foto von dem Auto (das Foto vom Auto)
   • das Foto des Autos

3. "the photo of you"

   • das Dufoto - I think that is a nonsense.
   • das Foto von dir
   • das Foto des dein - I think that is a nonsense too.

4. "the president of France"

   • der Frankreichspräsident
   • der Präsident von Frankreich
   • der Präsident des Frankreichs

5. "the beauty of Prague"

   • die Pragschönheit
   • die Schönheit von Prag
   • die Schönheit des Prags

My conclusion here: it is not possible to state a rule for every expression. (E.g. "photo of XXX" should be translated only using b) in the 3) sentence, but in the sentence 2) all options a, b and c are possible - it also depends on what you are taking a photo of.)

Questions:

• What are your thoughts about these sentences?
• What is your idea of a rule how to translate "of XXX" into German?
• A German friend has suggested the option "Frankreichs Präsident". Is this a form of the genitive? If yes, where is the word "des" here missing (same for "Prags Schönheit")?

Answer 1

A compound noun is a possible option for many cases, but you happened to pick 5 exemples where it is not suitable.

1. the color of the car

   • die Autofarbe - As @guidot stated in his answer, that would rather mean the paint for the car (even though der Autolack would be more usual)
   • die Farbe vom Auto / die Farbe des Autos - both are ok.

2. the photo of the car

   • das Autofoto - very unusual. People would probably guess it means a photo that was taken by an automatic device.
   • das Foto vom Auto / das Foto des Autos - both are ok.

3. the photo of you
   You correctly guessed that #1 and #3 are nonsense. Das Foto von dir is fine, as well as Dein Foto as suggested in @mic's comment.
   Note that both could either mean the photo of you (you are on it) as well as the photo from you (you have taken it). You can only know which one is meant from context.

4. and 5. Since Frankreich and Prag are (proper) names, genitive works a bit differend here. It is expressed by the "s" added to the name (instead of the word des).
   Der Präsident von Frankreich, Frankreichs Präsident or der Präsident Frankreichs all are correct. Idiomatically you would often say der französische Präsident (the French president).
   Similar you could say die Schönheit von Prag, die Schönheit Prags or Prags Schönheit.
   There is also the form die prager Schönheit, but that would mean the beauty from Prague (a beautiful woman from there).

Answer 2

There is no easy answer on that one, since my dictionary lists 11 different meanings for of. While south of Paris also would translate to südlich von Paris this is only superficially the same word.

Some rules of thumb:

• use von if in doubt concerning the genitive - it will likely be understood
• Stay clear of forming new composite nouns: Autofarbe would more likely be understood as a paint for cars than as a color of a car. The answers to your question here still apply.
• Personal pronouns are seldom valid building blocks for compound nouns.