I am awful at remembering whether a noun is masculine/feminine! I thought I had this one, but nope. "un" instead of "une".
Why can't I use ''dame'' instead of ''femme''?
Because "dame" doesn't translate to "woman" in any way. I just looked it up and the google translator shows "woman" as one of the possible translations for the German "Frau", but not for the French counterpart.
I wrote "la femme écrit une lettre seule" without the comma. Would that imply that the woman wrote a sole letter, or does the word order have to be "une seule lettre" for that?
I put Seule at the start of the sentence, would this have suggested that the woman was one of a group and she was the only to have written?