In that case there would be an article before the word

Not any more than "He sees deer." would mean "He sees a deer." You would have to put the article for the singular. "et brev" indefinite singular or "brevet" definite singular, but "brev" by itself is indefinite plural.

That would be: He's reading a letter = Han leser et brev

That doesn't make sense.

No, it means "He is reading letters".