It could be; but are is more natural.
Because of that, you would only use will be to indicate that something is likely to change. So
When you've finished your degree there might be other things you will be interested in.
suggests that something will have changed (in you, or in the world) by the time you've done your degree, to give you these other ...
The difference between the two is that “when” implies certainty. You are sure your son will complete his work, and then you will go to the restaurant.
“If” is uncertain. Your son might complete his work, or he might not. If he does, you will go to the restaurant.
Also, you need to add “the” before “restaurant.”
Yes, all those sentences are grammatical.
By tomorrow, he will have left Paris. When tomorrow comes, he will no longer be in Paris. It doesn't say exactly when he will leave.
I will leave Paris by tomorrow. I promise/intend to leave tomorrow or earlier.
I will have left Paris by tomorrow. I confidently predict that when tomorrow comes, I will no longer be in ...
Expanding on Lambie's comment, yes, "I go to bathroom then I come to bed" is wrong in the case you're describing.
If you're telling your daughter what you're about to do, "I go to the bathroom then I come to bed" isn't right, because it's present tense - it sounds as if you're already doing both of those things now, but you're not. Since ...
If something has not yet happened in the future.
The movie will have started by the time we get to the theater as it'll take us 20 minutes to get there. [FUTURE perfect]
There is an event preceding the getting there in the future: the event is that the movie started before you got there.
Think of it as parallel to:
The movie had started by the time ...
Melanie starts school tomorrow.
Melanie will start school tomorrow.
are both correct. However, it is very common using present to express future, so your first example is the more acceptable.
However, there is another problem I want to emphasize:
Melanie will start school from tomorrow.
is incorrect, because there is no match between start and ...
The only interpretation under which he works late is possible here is meaning he always works late on Mondays: there's a strong implication that the hearers know this, or should know this.
The sentences you quote from the grammar book simply do not apply to this case, but I'm not clear why not. I'll think about it.
Edit: I think I've got at least part of it. ...
No, this isn't describing the future. This falls under the "Actions started in the past and continuing in the present" use of the present perfect as described here: https://www.ef.edu/english-resources/english-grammar/present-perfect/ .
No. In English it is very common to use the present tense to refer to an activity that will actually happen in the future.
You can think of it as meaning:
Sorry, I have to work [at that time]. I don't have the time [then].
I might use "won't" instead of "don't," but definitely not "will have" instead of "have."
The "will" says the proof will happen in the future. The "now" says it's in the immediate future: right now, the next thing in the paper.
You could leave out the "will" without changing the meaning. If you leave out the "now" but proceed directly to the proof the reader may be a little puzzled.
Both your sample ...
It is intolerable to think of this storm of universal distress leading up to nothing but some "conference" of diplomatists out of touch with the world, with secret sessions, ambiguous "understandings".
lead up to something is a phrasal verb. leading up to something is its present participle form.
— phrasal verb with lead verb
If a ...