"Я собираюсь продолжить этот рассказ."
Translation:I am going to continue this story.
Yes. But not literally. Literally, "continuation follows." But it is used like the English phrase. "Когда заканчиваешь смотреть любимый сериал онлайн, всегда ждешь заветной надписи «Продолжение следует», даже если известно, что оно не запланировано." http://www.ivi.ru/watch/prodolzhenie_sleduet
If "I am going to continue this story" is acceptable, why not 'I will continue this story."?
"Собираюсь" means "I am going to" in a sense of "I am planing to", but it doesn't mean "I will". Planning to do something is not the same as to actually do it.
As my English teacher said the sentence with "I will" says that you had had an idea of doing it just before you said that and that it is not really planned. While I am going to" means that you have planned it at least for some time and you prepare for it. Also if we speak about future "I am continuing the story" (or to avoid strange words "I am writing the story") means that either it is done on strict schedule or that you decided to do it no matter what. (!) ^Please correct me if I am wrong (!) So having said that the closest translations for those cases would be 1. I am going to... - Я собираюсь.. (kinda I am preparing in literal translation) 2. Я продолжу - I will continue 3. Я продолжаю - I am continuing
It's a "good for all" solution, as it can be anything. Whatever it was according to your context.
As a native English speaker I consider "I shall do x" to mean "I intend to do x", with the conditional sense of "shall" conveying the idea that of course events may intervene to prevent me.
It can also be a simple prediction: if you do not come to my party, I shall be very disappointed. I would use “shall” only with the first person with this meaning, probably because there is some intention involved, as you say. When shall is used with the second or third person it has the sense of obligation or promise. It occurs in rules and legal prescriptions: Thou shalt not . . . Or “If the judge so rules, the prisoner shall be released.” Will would be simple prediction but shall states an order.
Future expressions on English are very complex and depend heavily on context. It’s hard to make a rule that covers all incidences. For example, one difference between « Will » and « going to » is that will/shall is more formal. Whether you ask “Will you be here tomorrow?” or “Are you going to be here tomorrow?” is a matter of style, probably depending on who is being addressed and whether you are speaking or writing.
Another difference between will and going to is that will is a less immediate future: it will rain vs it’s going to rain. The former indicates a vaguer time frame. Also will is used more comfortably with abstract conditionals: “If you press too hard, the handle will break” vs an immediate real possibility “If you keep pressing like that, the handle’s going to break.” Getting far afield here, but future expressions are my favorite English grammar subject.