In this case den is not a formal subject, but a real pronoun referring to some object. With no context, we don't know what gender it is, so both work here.
Och... den är borta! http://www.retecool.com/wp-content/uploads/2014/05/poofanditsgone.jpg
Yes, borta refers to things that are gone, lost, away, whereas bort is a more general adverb meaning away. The distinction goes back to Old Norse burt and burtu, interestingly.
Because it answers to the question ”where”, then it’s an ”adverb of place”.
"That" generally refers to something that is present, so "that is gone" sounds a bit like a contradiction.
“That” in English can also refer back to a previous referent. “I don’t like this bike; can I have the one I used yesterday?” “No, that’s gone today.”
I guess because you wouldn't really say that in English, at least not with the same meaning as "it's gone."
This is the first time in a while I couldn't hear the r at all. I know it's different in Swedish but this seems completely like "bota" or "botta" to me. Thankfully, it accepted my answer as a typo, but it really doesn't sound quite right.
borta actually sounds pretty good here. The present TTS isn't that good with r sounds generally, but here I think it sounds very natural. Compare with native speakers here: http://sv.forvo.com/search-sv/borta/
In Standard Swedish and most dialects, R melts together with consonants D, T, N, L and S to form what is sometimes called retroflex consonants (aka supradentals or postalveolars).
English Wikipedia has good articles on those, follow the links from the table here
This one is about RT: https://en.wikipedia.org/wiki/Voiceless_retroflex_stop
If "gone" is not an adv. in English, I think "bort" more like "weg" in German in its meaning. Den är borta = Es ist weg. In this German case it should also be an adv.
How would you say "It is away"? Because "gone" means non-existent but "away" means somewhere else but not here.
I thought it was "They are gone." Because de, den-- pronounced the same? And borta-- plural? Nej?