Learn Hardcore Japanese: tyouzyou de hirugohan wo tabemasita.

山頂 (さんちょう) – literally “mountain summit,” very common in hiking contexts
頂点 (ちょうてん) – “highest point” in a more abstract or literal sense (not always a physical place)

Why is the particle で used after 頂上 instead of に?

In Japanese, で marks the location where an action takes place, while に marks a destination or a point in time. In 頂上で昼ご飯を食べました。, you’re saying “I ate lunch at the summit,” so you need で (location of eating).

頂上で写真を撮った。 (I took pictures at the summit.)
頂上に着いた。 (I arrived at the summit. – destination, so に.)

Why isn’t there a subject like “I” or “we” in the sentence?

Japanese often omits the subject when it’s clear from context. Since you are speaking about your own experience, you don’t need 私が. The sentence implies “I” by default:

（私は）頂上で昼ご飯を食べました。

Why do we use を with 昼ご飯 here?

を is the direct‐object marker in Japanese. It marks what is being eaten (the object of 食べました).
Structure:
Subject (omitted) + Locationで + Objectを + Verb.

What tense and politeness level is 食べました?

食べました is the past tense of 食べます (“to eat”).
It’s in the polite form (ます‐form).
So 食べました = “(I) ate” (polite).

Could I say お昼ご飯 or just 昼ご飯? What’s the difference?

お昼ご飯 adds the honorific お, giving a slightly more polite or “softer” tone.
昼ご飯 is perfectly neutral and common in conversation.
Either is fine:
頂上でお昼ご飯を食べました。
頂上で昼ご飯を食べました。

Can I swap the word order to 昼ご飯を頂上で食べました?

Yes. Because Japanese relies on particles, you can reorder the phrases as long as each noun keeps its particle:

昼ご飯を頂上で食べました。
頂上で昼ご飯を食べました。
Both mean “I ate lunch at the summit.”

Instead of 昼ご飯, can I use ランチ?

Yes. ランチ is a loanword from English and is commonly used, especially in casual or restaurant contexts:

頂上でランチを食べました。
Just be aware that ランチ often evokes café or restaurant lunch, whereas 昼ご飯 is more general.