French language Q&A Forum

Is there any general rule about how to identify which French expressions do not use an indefinite article where English would use one. In other words, why not "c'est un bon signe" ?

Someone presented the example, "merci de m'aimer" which I believe means, "please love me" rather than "thanks for loving me" and directed them to this lesson. However, "merci de m'avoir aimé" doesn't, in my mind, capture the sense of "thanks for loving me" as an ongoing action/effect.  After digging further, I found some texts such as, "merci de m'aimer autant" and "merci de m'aimer" on reverso. I'd like to test my instinct and the found examples. Is this an exception where the construction will retain the sense of thanks rather than a polite request, due to context, or are these examples incorrect?

Tangential follow up question: I understand "du cadeau" will be interpreted sarcastically, but is this only for physical gifts? For example, I have found a bit of text with "merci du cadeau de ta présence". Does the modification into a more conceptual gift change meaning, or is this simply incorrect, wanting instead, "merci pour le cadeau de..."?

Merci de m'éclairer! 

Should this be "il l'a oublié"? It sounds weird without a direct object for oublier.

I don't understand "arrivés" at the end of the sentence. Is "on est" understood?

Est-ce que tu veux que je prenne de la crème solaire ou est-ce qu'on en achètera une fois arrivés ?

From the quiz - C'est les soldes, je vais faire les magasins.

Why is faire used here instead of fais?