musieć means 'must', yes. But also "to have to, to need to, to be obliged to". And as it is used in conditional, it's hard for me to imagine a phrase like "We would must"...
"must" is only used in the present or perfect, and is never used with a modal verb, so it's "will have to, would have to, may have to", etc.
Why not "We should make lunch"? In this context, "should" means basically the same as "would have to".
That's not what the Polish sentence says, and I believe that's not what "would have to" means.
The Polish sentence is something like this: "Come on, you really want to invite your mother? We would have to make lunch, we would have to clean the house... I don't want to do this all!"
I can assure you that "should" definitely covers the meaning of "would have to" amongst many others. "Should" originated as an inflected form of "shall", while these days it's most often used without any conditional sense at all, the conditional, past and even subjunctive uses of "should" are still totally valid.
Sorry, but they don't mean the same. "We should make lunch" simply expresses a mild obligation, and has no suggestion of condition.
Duo's sentence expresses the result of an unstated condition, for example:
"If they let the kids out of school early, we would have to make lunch"
You're only considering one of the many meanings of "should". It can certainly suggest the conditional, after all, it originated as the conditional form of shall.
'We would've to make lunch'? That doesn't even make sense. It's bad grammar at the very least. It should be 'We would have HAD to make lunch.'
I don't see why it would be wrong, it's conditional and refers to some (potential) future.
"Kate wants to come on Sunday? Come on, I don't want her here! We would have to clean the house, we would have to make lunch... That's too tiring!"
Now I guess that maybe you just referred to "would've". Well, such contractions are accepted automatically, there's really no way to block them...
"obiad" means both, depending on which variety of English you use.
śniadanie/obiad/kolacja is either breakfast/lunch/dinner or breakfast/dinner/supper.
Polish people usually know the second version, we use the first one here because it's more American and Duolingo is an American company.
All those versions work, you may answer "dinner".