But "Why don't we ...?" is also used as a suggestion, rather than literally inquiring after a reason.
"How about eating pasta?" "What do you think about (eating) pasta?" "Why don't we eat pasta?" "Shall we eat pasta?" "Let's eat pasta!" are all more or less synonymous.
Yes, the translations are too strict.
And generally, do not allow for British English, where it is common to say "I/we shall" but this is not accepted as a correct answer and only "I/we will" is accepted.
-(y)elim mi? is "shall we?" -- that ending is specific to "we".
Only if the suffix starts with y-, I believe, so you have e.g. future yiyecek and present continuous yiyor but past yedim and passive yenir.
Because -elim does not mean "we are ...ing"; it means "let's ...!" in a statement and "shall we ...?" in a question.
"We are eating pasta." would be Makarna yiyoruz.