Hi Vannee,
Yes, I think Simon makes a fair point – I’d say that you can almost always use “will” instead of “shall” and not have to worry about it, but it doesn’t really work the other way around; “shall” is really only used in quite formal and polite settings, and not very commonly now.

Hello Vaanee, I think the best way for me (or any other experienced teacher of English) to resolve your confusion is to ask you: What have you been taught so far about the use of ‘shall’? ‘Shall’ is not even included in the list of ‘correct future tense forms’ at the head of this Future Tense Exercise, which indicates, quite correctly, that in modern English it is used only in a limited number of situations.

Hi, sorry for the very slow response; there’s flexibility here. Generally I’d say the key difference is that the going to form carries a little more emotional emphasis, e.g. to show intention or a belief, where the present continuous merely shows a plan, but in practice they can often be interchangeable.

II don’t understand when do I use going to and when I use the present continuous both are for personal arrangements in the future

Hi Chloe,

Sorry for the slow response. They are good questions, which provide quite subtle/nuanced answers.
26 – you can but it would change the meaning slightly; “I will live” puts more emphasis on being determined to do it, while “I will be living” would typically mean you expect to be in process of it (more a neutral fact).
28 – yes, you could say “are you taking”, again with a slight difference that “are you going to take” / “will take” would suggest a determination/intention whereas “are you taking” is a more neutral plan (i.e. it’s established). In both these cases, however, there may be little real difference in how they are interpreted.
30 – no, this one is different, because we have “now” – “I am checking” would mean you are in the process of it, whereas “will/am going to check” suggest you are about to start.

It’s quite rare, I would say; it’s mostly just to demonstrate a time duration to a point in the future, which is not something we do very often.

With apologies, my initial reply to this was brief and unhelpful – both of these sentences are grammatically correct but would require a particular context to be used. Most likely in both cases the simple future would be more appropriate (“I will wait” / “I will meet/am meeting”) – unless you wish to discuss the meeting being in progress at 8 or the process of waiting for the bus (usually to discuss the duration). Though ultimately it depends on context, so feel free to share more information about the sentences and what you wish to express.

Simon also wrote this explanation: these sentences are not grammatically bad, but if placed in their most probable context they are deviant. In a probable context the first would much more naturally be ‘I will wait in the shelter until the bus comes’ (i.e. not merely a prediction but a declaration of intention), and the second would more naturally be ‘I’m meeting my friend on Friday at eight (o’clock)’ (i.e. not only expressing a declaration of intention but announcing that this meeting has been arranged with ‘my friend’).