Outside I see a writer.... nem, jó? Why does outside need to go on the end?
"I see a writer outside" is just the "standard" English way of saying this, I think. But "outside I see a writer" is correct as well. I would only use that variant if I wanted to stress "outside", though.
Now I'm confused --- I thought the general assumption was that in Hungarian, the word immediately before the verb was the focus. So isn't "kint" the thing being stressed? How would I say the sentence if I wanted to stress "kint?"
If there is a focus, it's the part of the sentence right before the verb, yes. But there does not need to be a focus, in which case the sentence is more neutral. For verbs without prefixes, like "lát", there is no way to tell from the written form whether the focus is empty or not. (For verbs with prefixes, the prefix shifts.)
In spoken language, stress makes it possible to disambiguate this: If there is a focus, it is typically stressed. In the audio for this sentence, the speaker does put this stress on "kint", so it's the focus. If it weren't in the focus, it would not be stressed, and typically there would be a bit more stress on the verb.
So yes, there is a strong case for "outside I see a writer" here. Still, even in English you can say "I see a writer outside" with the stress on "outside", with the same property that there is a stress that is not reflected in writing.
I think the writer is - you could be either inside looking out at him, or somewhere else entirely e.g. watching from afar on a security monitor. Without context, either is possible.
For the English sentence yes. How could I write in Hungarian that I while ouside see something?
az írót (the one writer you're looking for): use látom. egy írót (any old writer will do): use látok.
If there's no subject at all, you can default to látok (though it seems there can be nuances if the subject is implied). However if there is a subject, you need to ask the followup question about whether the sentence talks about a specific item (the writer) or a general class of item (a writer). In this case it's the latter.