When you confuse skriver with spiser and it reads "I am eating a letter" Alphabet soup maybe?
You can write a letter in pencil. To pen requires, well, a pen. They are similar but not the same.
The translation "I pen one letter" as the answer. More natural sounding English would be I am writing/I write the latter.
I really don't know why that sentence was given as an alternative translation (bad machine learning???) because et can't be translated as "one", only as "a/an". The correct word for the numeral one  is ett (for nouns of neuter gender).
As for the verb "to pen", that is a valid translation, but much less common than "writing/writes" and is a consequence of variations in English vocabulary.
Depends on the gender. Here, letter is neuter so you use "et". For other words (masculine or feminine) you use "en". Ex: en skogen (a forest) Et bord (a table)
And just like many languages, you can't guess the gender, you will have to learn it for each word. :)