"du" question; "à le + [noun event]" as meaning "at the [noun event]"?

Question

The following was an advertisement that I saw earlier today at the post office:

Obtenez GRATUITEMENT le service de réacheminement du courrier pendant un mois à l'achat d'un abonnement de 12 mois.

Get one FREE month of Mail Forwarding when purchasing 12 months of service.

1.

le service de réacheminement *du* courrier = "Mail Forwarding [Service]".

I do not know why it is du instead of de.

My understanding is that "de" is used to describe the kind or use of a noun:

• "la chaise de chien" = "the dog chair"
  (ie, "dog" is a kind of adjective that describes the specific kind of chair. it's not all chairs in existence that you're talking about -- it's those that are "dog" chairs).

and that "de + le/la/les (or de + mon/ma/mes etc)" is used to describe possession:

• "la chaise du chien" = "the dog's chair"
• "la chaise de mon chien" = "my dog's chair" (ie, the chair belonging to my dog).

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For example, the "de" in "le service de [mail forwarding]" makes sense. It's not every kind of service in existence that I'm talking about. It's the mail forwarding services I'm talking about; mail forwarding is a kind of adjective to "service".

In this way, it sounds like "Mail Forwarding" should be de (ie, "réacheminement de corrier"), because "Mail" is a kind of adjective that describes "Forwarding".

Question 1: Why is it "réacheminement du courrier", instead of de?

2.

The English group-of-words "when purchasing 12 months of service" is translated with "à l'achat d'un abonnement de 12 mouis".

This is a sentence construction that I am unfamiliar with. I am trying to understand it.

I understand that "l'achat" means "the purchase". I'm unfamiliar with the construction 'à + [noun that describes some event (such as purchasing something)]" to mean "at the time [noun] happened".

Question 2a: Can you give me more examples of this construction?
Question 2b: Can you give me a website that explains this usage of à ?
Question 2c: Are there other ways of translating "when purchasing 12 months of service", such as "quand vous achetez un abonnement de 12 mois" or "en achetant un abonnement de 12 mois"?

Question 3: Would the sentence still be correct if we replaced "pendant" with "de"?

Answer 1

Question 1 :

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I think that you are right. Saying de would not be grammatically wrong. But I think du is used because the mails that are forwarded are not just any mails. For example, in un service de réacheminement de courrier here the de would be prefered because it's indifinite.

Question 2 :

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Some examples :

[...] des hommes mûrs pleuraient à la vue du drapeau étoilé soutenu par tout le corps de ballet noyé sous les clartés des projecteurs. (H. G. Wells, La Guerre dans les airs)

Il recevra un cadeau à l'obtention de son diplôme.

I did not find any website but I can tell you that à is used as a complément circonstanciel de temps. Which means that it decribes the moment, here following on an action/event. So you could remplace it by :

Lors de l'achat d'un abonnement de 12 mois

Suite à l'achat d'un abonnement de 12 mois

Après avoir acheté un abonnement de 12 mois

As you suggested, it can also be replaced by :

Quand vous achetez d'un abonnement de 12 mois

en achetant un abonnement de 12 mois

Question 3 :

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No. But Yes if the sentence was :

Obtenez GRATUITEMENT un service de réacheminement de courrier d'un mois à l'achat d'un abonnement de 12 mois.