Yes,that would be ''Neden makarna yemiyoruz?''
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.
Is there a Turkish way to say "Shall I...."(i.e. a retorical question) For example: Shall I eat pasta? Or: Should I go home now?...Or: Should I take my medicine?
Yes, you could ask your father, if you should throw out the trash for example:
"Çöpü atayım mı?"
does the "e" in "yemek" always change into "i" when connected to suffixes ?