the phrase "a day" in English should also include the translation "κάθε μέρα" in this example, or no?
Given that there is better word-for-word matching I'd say no. In this context, I do this:
per day = ανά ημέρα
a day = τη μέρα / την ημέρα
every day = κάθε μέρα
I agree. In this context doesn't suit to use κάθε μέρα.
Ο εργαζόμενος τρώει δύο αυγά την ημέρα. it is correct
why is wrong "Ο εργάτης τρώει δύο αβγα τη μέρα
It's correct and added now as a possible translation. Thanks
I don't understand why "μία φορά την ημέρα" but "δύο αυγά ανά ημέρα". Maybe the meaning of both ("tin" and "ana") is similar?
Are you asking if both translations are correct? If so yes they are both correct.
A different question to those above. Why is ο εργάτης φάει.... Not acceptable? Can 'φάει' not be used in this context?
The verb τρώω is irregular and φάει is the subjunctive form of the verb, hence it’s wrong. Plus φάει cannot be used without να/θα or the auxiliary verb έχω. See here the conjugation of τρώω: https://moderngreekverbs.com/troo.html