"The women are writing letters to us."
Translation:Les femmes nous écrivent des lettres.
Les femmes nous écrivent des lettres à nous? "The women write us letters to us?" No, that's extremely redundant. And just having Les femmes écrivent les lettres "The women write the letters" (First of all, notice how you've changed des to les and thereby added "the" into the translation) leaves out any indication that the target audience of the letters is "us".
I can't think of any instance in which you would say à nous, because that combination must become the indirect object pronoun nous placed before the conjugated verb. It's required, in the same way that you can't say de le - that combination must become du. It's not optional.
(There is one exception for à nous, but it doesn't mean "to us"; it means "ours" and is synonymous with le nôtre, e.g. Le victoire est à nous! "Victory is ours!")
I personally think, because even though, as you said, it's countable "les lettres" would mean "the letters" and, as you may know already, "la/le(s) - the" is used when you mean a noun (thing or being or idea), which has been already mentioned or you already know about, which one in particular you are aiming towards. "De(s)/du" is, so to say, the word for "some" and it's also, as in English, used for (un)countable nouns, but we don't intend to aim to one directly or hasn't been mentioned or an unknown amount of a noun (e.g. An apple, Two apples, Some apples, Any apple). So, long story short:
"La/Le(s)" means "the" and it's used, when the noun has been mentioned, one in particular;
"De(s)" means some" and it's used when we don't know or care about the nouns amout.
-I hope it helped.
"On" is a personal pronoun meaning "one" or "someone", or sometimes replacing "nous". It has no role in this sentence.
"Are writing" is a continuous present tense, which does not exist in French as a verbal form. To translate "the women are writing", you have to use the French present tense "écrivent". Context would distinguish the meaning of "are writing" from "write" in simple present.
TanAnthony21, I thought that was a good question. The Wikipedia page en.wikipedia.org/wiki/French_personal_pronouns has a nice table showing how "on" and "nous" work in colloquial speech.
direct object: nous
indirect object: nous
According to that table "on" is not allowed here, because "on" can only be the subject of a sentence.