Repeated “a”, and “dativo de interés”

Question

(1) In this sentence the personal “a” is repeated: “ A Pedro y a Pablo les cantaron una canción por su despedida”.  
However in this sentence the second “a” is omitted: “ (Les) cantaron una canción a Pedro y Pablo por su despedida.”
 Is the second “a” arbitrary or is there a rule for when to omit it?  
(2) I notice two uses of IO pronouns in the examples and questions. 
The first is the common usage such as giving something to someone, saying something to someone, or taking something from someone. This usage always has a direct object. 
The second usage is from a lesson from a higher level, called the “dativo de interés”, which has an entirely different meaning altogether. Instead of always having a DO and giving the DO to someone, there may not be a directobject at all (intransitive verbs), and the IO simply emphasizes that someone is affected by the action.  
Sometimes there is a DO: Mi hija pequeña no me come nada.
 and sometimes there is not:  Ayer nos cayó un buen chaparrón.
 
 
Inma’s answer to Thea reflects this type of usage.  
https://spanish.kwiziq.com/revision/grammar/dativo-de-interes-specific-use-of-indirect-object-pronouns
 
 So there are different layers to the usage of the IO. 
 Could you make a lesson contrasting the different types of IO usage? It could be useful for many of us.

Accepted Answer

Hola Marcos
For your question 1., the second "a" is omitted simply because it's implicit. You can add it too - both are fine: Les) cantaron una canción a Pedro y a Pablo por su despedida.”
For your question 2., the sentences using the dativo de interés can have a DO or not. In the sentences you posted as examples I can see the DO in both:
Mi hija pequeña no me come nada. 
¿qué es lo que no come? nada (DO) 
Ayer nos cayó un buen chaparrón. 
¿qué nos cayó? un buen chaparrón (DO)
But this is another sentence from the lesson on dativo:
Los niños se nos están haciendo mayores sin darnos cuenta.
Hacerse mayor is a intransitive verb and there is no direct object here.
Note in the first sentence that "nada" in the previous sentence could also be considered an adverb of quantity in my opinion as in ¿cuánto me come/no me come? nada
As for the suggestion for a contrasting lesson on the indirect object pronouns, it'd be very interesting, but that type of content would be very difficult to "test" in our quizzes as you'd need a lot of context explained and there is no space for that, unfortunately. However, an article on the different functions of the Indirect Object pronouns is something to be considered, of course. It's been noted. 
Gracias por la sugerencia.
Saludos 
Inma

Answer

Thanks Inma. An article like that would be very helpful.