"per" needs to be added. The other options don't work in this context.
"A" should not be, because it doesn't really mean "a". It's one of those cases where you can use a less literal translation. It actually means "per day". "A day" is only acceptable because we often change "per day" to "a day" in informal speech in English.
It literally means "per" in this sentence. It's just that "one _ a day" is used informally in English to mean "one _ per day".
Per should be included as an alternate translation for por. (Usually "de" means of, and "por" can mean by, for, etc., but prepositions are tricky and do not always translate consistently across languages.)
It changes the meaning a bit to talk about frequency during the day, rather than how often someone eats an egg in general.
We can see this more easily when we increase the number. Once a day versus one per day next to twice a day (perhaps one each at breakfast and lunch) versus two per day (maybe both of them in the same meal).
It would be rather unusual in daily speech for someone to say "I eat one egg per day". This is a literal translation from Portuguese produced by DL's software.
"Per" is encountered in formal documents, reports, etc. Unless we want to be emphasize enumerating items, "a/an" is what one hears in spoken English..
I eat an egg a day. - I eatan eggaday. (It makes English smoother.)
Miles per hour; miles per gallon; liters per 100km; per diem; price per person; calories per serving; servings per container, or in question forms, how many pieces per pound; how many trains per day; what is the price per liter; what is the budget per day; and so on. I think putting a/an before any of these would be stretching English a bit (though it is often done).
There are lots of ways to say the same thing. An egg a day; an egg each day; an egg every day, one egg per day; and there really is no wrong or right among them. Something used formally, does not mean it cannot also be used (and well understood) in everyday conversation.
I think perhaps the flow you are getting from your preferred method comes from the English idiom of, An apple a day keeps the doctor away.
But this exercise is not a Portuguese construction:
Yo como un huevo al día
Ich esse täglich ein Ei.
Io mangio un uovo al giorno.
Я ем одно яйцо в день
آكل بيضة واحدة في اليوم
나는 하루에 계란을 한 개씩 먹습니다
There are more (especially for learning English from other languages), but each of them have "one" and "per" in the sought solution (or to translate from).
Which flows with your idea of emphasizing enumeration (not an everyday word in itself :D).
All your many links point to DL software taking the same English sentence and translating it. That does not prove anything about what is natural, spoken English.
As I mentioned, per is encountered in documents, schedules, newspaper articles and scientific texts, but is less common in spoken language than using "a/an". Linking words via connecting sounds to achieve a certain smoothness and rhythm is an essential part of the spoken language.
"I eatan eggaday " is easier to say than "I eatan egg per day." The consonents link with the following vowel to smooooth out the language and make it less choppy. Sometimes new sounds are created when consonents and vowels are linked. This is not "my" preferred method. There are many textbooks devoted entirely to this facet of learning since it is an essential component of teaching ESOL. Rachel's English on youtube is a good site to hear more examples of connecting sounds to achieve natural spoken English. Here are two sites - British and American - that give a bit of information.
Previously you wrote:
This is a literal translation from Portuguese produced by DL's software.
Which is why I provided the links I did. This is a standard sentence from English used in several of the different language programs, so it is not a Portuguese translating issue. The "per" is original to the sentence.
For many saying, a day, an hour, a gallon, a person, and so on seems more awkward (and less refined) than per or each.
The great thing about English is there are several ways to say things (just ask the Brits, Kiwis, Aussies, and Canucks). Very few phrases need to be said exactly as one person (or even dozens whether they present as experts or not) believes they should be. Language is not religion.
Thank you for sharing those links. :)
There is a difference between "everyday" (no space) and "every day" (two words).
"Everyday" is an adjective and can only be used to modify a noun. "Her everyday breakfast is an egg with toast", "She eats breakfast at 7 as a part of her everyday routine." "Every day" can be used as an adverb phrase with the same meaning as "daily". "I eat an egg every day" (two words) should be accepted. If it's not, report it.