I just got a mistake for submitting "cannot" instead of "can't". That should be accepted.
It sounds very unnatural but would technically be correct. Just as in English we'd say "let's party!" And is sounds strange to say "let us party!" The first sounds like a suggestion or command and the second sounds more like a plea but could also be the same as the first. It just sounds so unnatural because it's old-timey and rarely, if ever, used.
I wrote: "He can't read either?" and it was a mistake. However, I'm quite sure it is a correctly formulated sentence in English. It's called "inversion" I think and depends on which word you put the accent on. (The word "either" in this case.)
"He can't read either" is a statement. To ask a question, indeed you have to do the inversion, and it would look like that: "Can he not read?". Since there is a question in the exercise (Kan han ikke lese heller?) you can't translate it as a statment. :)
This would work as a question, depending on the intonation and the stress. With a rising intonation on the last word, as you stated, you get a common way of making a question out of a statement.
Does this "either" means that there are two things he can't read, or does it mean that reading is another thing he can't do?
"either" refers to a choice between one thing or another, so this "heller" should translate as "neither", but it more natural to say "can he also not read?"
He can't write; he can't read, either.
She can't read, and he can't read, either.
Using neither, my first example would be, "He can neither write nor read.
In the second example, neither can't be used, except to say, "Neither can he."