"J'ai demandé du sel après qu'elle m'a donné du poivre."
Translation:I asked for some salt after she gave me some pepper.
You write "donnée" when the direct object precedes the conjugated verbs. Here m' is an indirect object, the direct object is "poivre." She gave du poivre (to me). "Poivre" is the thing that was being given, m' or me is the person receiving it.
Here is an example where the direct object precedes the verb in the past tense:
Voilà la clé que je t'ai donnée. "La clé" is feminine and it proceeds "ai donnée," therefore donnée is in the feminine past participle form.
Because French is French and English is English.
The two languages share a significant number of Latin based words, but the meanings have evolved differently over hundreds of years in France and in England. That is why yes, there are many words that are the same, but there are also words that look the same but mean different things. Beware of "faux amis."
To demand something in French you could use the verbs
exiger/to require or
ordonner/to order (ordonner quelqu'un de faire quelque chose / to someone to do something)
Here too is another false friend. "Ordonner" does not mean to order something in a restaurant. For that you'd use the verb "commander."
Je command un sandwich. → I am ordering a sandwich.