Learn Danish: Jeg sidder og skriver netop dette bogstav.

Here, netop acts as an emphatic focus adverb meaning "exactly" or "precisely". Placing it directly in front of dette bogstav strongly emphasizes that the speaker is writing this exact letter, deliberately ruling out any other options.

I thought the word for a written letter was brev. Why use bogstav here?

Bogstav refers specifically to a letter of the alphabet (like A, B, or C). A brev is a message you write and send in the mail to someone. This sentence means the person is physically writing a specific character of the alphabet.

Is it strictly necessary to use the sidder og skriver continuous structure here?

No, you could grammatically just say Jeg skriver netop dette bogstav. However, using a position verb like sidder (sit) plus og is the most natural Danish way to emphasize that you are actively in the middle of doing it right now, much like the English continuous "-ing" form.

Why do we use dette instead of denne in this sentence?

Because bogstav is a neuter noun (et bogstav). The demonstrative pronoun for "this" must agree with the gender of the noun it modifies, making it dette.