I eat "at" around 12 o'clock

Duolingo for some reason completely skipped over particles.

Prepositions come after what they modify. For this reason, Japanese is said to be a postpositional language. In this sentence, に is the preposition. It means in or at. So this sentence could be literally translated as "12 o'clock about <=at eat." The subject is implied based on context, so we could translate it as "at about 12 o'clock, [subject] eat(s)." I hope this explains a little!

十二 - twelve

時 - indicates hour

十二時 - twelve o'clock

ごろ - at around

十二時ごろ - at around twelve o'clock

に - indicates time

食べます - to eat (formal form)

食べる - to eat (informal form)

Then:

十二時ごろに食べます - I eat at around twelve o'clock. (Formal form)

十二時ごろに食べる - I eat at around twelve o'clock (informal form)

Gracias

Here you have found a kanji in the wild, with an accompanying hiragana. In the dictionary you'll find kanji have multiple pronunciations, in two groups. I'm not super familiar with the groups, but you can kind of think of it like "first Kanji", "other kanji".

Kanji often have multiple pronunciations, most commonly one derived from the Chinese name for the kanji character and one (or more) derived from the Japanese word for the concept written by the kanji. Duolingo gives one pronunciation in the "hint" but it may not be the one used in the sentence. The hint tells us this kanji is default pronounced "shoku" (I think) but as part of the verb "to eat", it's pronounced "ta", to form "tabe".

There are different readings for kanji depending on context. Chinese origin, Japanese origin (onyomi and kunyomi); in most cases though a Kanji's name (like the letter M in English, is called "em") is different than its reading (ie. M => "mmm"). Also, the reading in vocabulary is different depending on context yes, but also grammatical placement. For example, I've noticed that in the majority of cases the onyomi pronunciation is used for compound kanjis whereas the kunyomi is often used when a kanji stands alone with hiragana to form a vocab word. This is not a set rule though ;).

You'll probably need to add わたしたち if you want it to be we

I can indeed be we eat, if 'we' is implied. This also depends on the social status of your counterpart.

The subject is implied in the Japanese sentence, so it could be translated as "I/you/he/she/it/we/they".

Because in Japanese, unless specifically mentioned otherwise, the subject of the sentence is the person speaking. That's why you can generally omit 'watashi wa' so often.

So in this case you translate it with the implied 'watashi wa' into 'I eat at 12 o'clock".

"Ni" here means "at", as in "I eat at twelve o'clock". In grammatical terms, it's part of an adverbial (When do you eat?). "Wo" is used for the object (What do you eat? I eat rice. "Rice" is the object.) "Ga" is used for the subject, if it is not the topic (Who ate the rice? I ate it. "I" is the subject (and "rice" is the topic).).

If you'd change the tabemasu to tabemashou it should mean what you said.

It means "around" as in "around this time"

In this circumstance there's no difference. If it marked you wrong, report it.

Order. If it's 二十, or "two tens (plus zero)", that's twenty, but if it's 十二, or "(one) ten plus two", that's twelve.

For more practice, observe the patterns of even larger numbers: 二百 Is two hundred, 九千 is nine thousand, 一万 is 10,000, 一万千 (one ten thousand plus one thousand) is 11,000, and finally: 二万三千四百五十六 is 23,456. Two ten-thousands plus 3 thousands plus 4 hundreds plus 5 tens plus 6 ones. Note how each decimal digit has its own character.

Because kanji can have several readings and pronunciation based on their context. This is because they often come from Chinese originally, and the Chinese reading, Onyomi, might sometimes be used rather than the Japanese reading, or Kunyomi. Regardless of reading, they are often linked by the concept, in this case, the concept of eating. 食べ may be pronounced as "tabe", to eat, and also 食どう, "shokudou", or dining room. You can see that both these readings are dealing with the concept of eating, and also why you hear "shoku" when you might have expected to hear "tabe".

を marks the direct object in most cases. に is used here, to indicate a certain point in time. As the time is not which is eaten, it cannot be used with the particle を here.

You seem to have the katakana "ni" ニ there instead of the kanji 二 "2"
There's a slight visual difference depending on the font but the kanji is a bit taller ニ二

十二時 juu-ni ji - 12:00
零時 rei ji - 0:00
Both could mean "midnight" depending on if you're using a 12-hour or 24-hour clock. If you're using a 12-hour you'd probably use 午前AM or 午後PM to distinguish whether you mean noon or midnight.

れい means zero, 十二 means 12
On a 24-hour clock 00:00 is midnight, the start of the new day, 12:00 is noon, a normal lunch time.
On a 12-hour clock both midnight and noon can be written as 12:00.
So when telling time, both can be 12, but only midnight can be written as zero, れい

ごろ: "(approximate) time; around; about; toward". Use it after a time, but before the に to indicate an approximate time frame.

Because you added the verb "go", it is incorrect. Your sentence would look more like «十二時ごろ食べに行きます。» Notice the inclusion of 行き