Can it really be 'must'?

Question

I've found this lesson quite difficult! The first set of examples ("Look at ..."), and most of the rest, sound very odd in English, and it's only Gruff's answer from five years ago that makes it clear that the phrase or sentence would not normally stand alone. Could more (or all) of the examples be made to make this clear? Also, in the first couple of examples (where there is an introductory sentence), the English translation is "... must have ..." and everywhere else it's "... will have ...". I think that the 'must' is wrong, but it's at least confusing! Hoping to help ...PSI now see that a similar discussion about contextual examples has taken 
place and been acted upon in the companion lesson (on irregular 
participles).

Accepted Answer

Thanks for the feedback, Andrew. We'll update the examples to make them clearer with a little more context.
 
Regarding "must have had to" vs "will have had to", this is really about freedom of choice in translating modal verbs to idiomatic English, which hopefully will be clearer with more context. 
For example, if you imagine somebody wondering why their sister hasn't arrived somewhere yet, they might say:
"My sister isn't there yet. She must have had to stay later at the office."
or, 
"My sister isn't there yet. She must have needed to stay later at the office."
 
"My sister isn't there yet. She will have had to stay later at the office."
or,
"My sister isn't there yet. She will have needed to stay later at the office."
They can all be used to express the same idea in English, but the latter two choices more closely match the French syntax in this case, "Ma sœur n'est pas encore là. Elle aura dû rester plus tard au bureau."
I think extra confusion arises here because in English we use "have" as both an auxiliary verb to express the past and past perfect, e.g. "I have/had " (and future forms) AND as part of the phrasal verb "to have to " which can alternatively be expressed using the idiomic modal verb, "must", which also expresses obligation or need. The syntax is quite different in English but the sense is the same.
More on modal verbs here:
https://french.kwiziq.com/revision/glossary/verb-types/modal-verbs-that-express-will-obligation-and-ability
Which translation is best depends what was meant and which direction one is translating.
Hopefully this helps!
All the best,
 
Gruff