Learn Hardcore Japanese: watasi ha natuyasumi ni kaigairyokou no keikaku wo kimemasu. - During summer vacation, I will decide on plans for an overseas trip.

This sounds like you’re emphasizing that I (and not someone else) am the one who will decide the plan. It answers an implicit question like “Who will decide it?”

So:

私は… = setting up “me” as the general topic.
私が… = focusing on “I” as the specific doer, often in contrast to others.

In most neutral contexts, 私は is more natural here than 私が.

What does に mean in 夏休み + に? Is it “in”, “on”, or “during”?

In 夏休みに, the particle に marks the time when something happens.

It can be translated in several ways depending on context:

in summer vacation
during summer vacation
over the summer break
for the summer vacation (when you mean “at that time”)

So:

夏休みに海外旅行の計画を決めます。
→ I will decide the plan for an overseas trip *during (or in) summer vacation.*

You can think of X に (do something) as “do something at/on/in X (time)”.

Why is there a の between 海外旅行 and 計画? What does 海外旅行の計画 mean exactly?

の often links two nouns in a “NOUN A of NOUN B” or “NOUN A’s NOUN B” relationship.

海外旅行 = overseas trip, traveling abroad
計画 = plan

So:

海外旅行の計画 = the plan *for an overseas trip / *an overseas-trip plan

Literally, it’s “overseas-trip ’s plan” or “overseas travel plan”.

Without の, 海外旅行計画 is technically possible as a compound noun (and you might see it in things like titles or business contexts), but in normal conversation and most writing, 海外旅行の計画 is more natural and easier to process.

Could I say 海外旅行を計画します instead? What’s the difference between 海外旅行の計画を決めます and 海外旅行を計画します?

Yes, you can say 海外旅行を計画します, and it’s natural.

Nuance difference:

海外旅行の計画を決めます。
→ Focus on deciding the plan that already exists as an idea or outline.
It suggests: “There are various options, and I will decide which plan to go with.”
海外旅行を計画します。
→ Focus on making or creating the plan.
It suggests: “I will plan an overseas trip” (actually doing the planning work).

So:

～の計画を決める = decide which plan / finalize a plan
～を計画する = plan ~ (create the plan)

Both are grammatically fine; choose based on what you want to emphasize.

What’s the difference between 計画 and 予定? Could I say 海外旅行の予定を決めます?

Both 計画 (けいかく) and 予定 (よてい) are often translated as “plan”, but they differ slightly:

計画 = plan in the sense of a designed scheme; more about the planning work, structure, steps.
予定 = schedule, arrangement; a plan that is set to happen at a certain time.

In your sentence:

海外旅行の計画を決めます。
→ Decide on the travel plan (how, where, how long, etc.)

You could say:

海外旅行の予定を決めます。
→ Decide the schedule/arrangements for the overseas trip (dates, maybe exact timing).

Both are possible.
If you’re talking about dates and timetable, 予定 feels a bit more natural.
If you’re talking about the contents and structure of the trip (route, activities), 計画 fits well. Japanese people often use both, sometimes interchangeably in casual speech.

Why is the verb 決めます used here? How is it different from 計画します or 決心します?

Meanings:

決める (決めます) = to decide something
計画する (計画します) = to plan something (create a plan)
決心する (決心します) = to make up one’s mind, usually about a significant personal decision

In this sentence:

計画を決めます = decide the plan (choose/finalize among options)

If you said:

夏休みに海外旅行を計画します。
→ You focus on doing the planning work during summer vacation.

If you said:

夏休みに海外旅行に行くことを決心します。
→ You focus on resolving internally to go abroad; it sounds more serious/emotional.

So 決めます is used because the sentence is about choosing / finalizing a plan, not about constructing it from scratch, and not about a dramatic life decision.

The verb is in non-past (決めます), so why does it mean “I will decide” rather than “I decide”?

Japanese doesn’t have a separate future tense. The non-past form (決める / 決めます) covers:

Present habit/general truth:
- 毎年夏休みに海外旅行の計画を決めます。
  → I decide my overseas travel plan every summer vacation.
Future action (when context is future):
- 今年の夏休みに海外旅行の計画を決めます。
  → I will decide the plan for an overseas trip this summer vacation.

In your original example, context implies it’s about something you will do in the future, so English translation uses “will decide”, but grammatically it’s just the non-past form.

Is it necessary to say 私? Do native speakers usually say 私は here?

No, 私 is not necessary. In Japanese, the subject is often omitted when it’s clear from context.

Very natural versions:

夏休みに海外旅行の計画を決めます。
→ If it’s obvious you’re talking about yourself, this is usually what people would say.

You only need 私は when you want to:

Contrast yourself with others:
- みんなは国内旅行に行きますが、私は海外旅行の計画を決めます。
Explicitly state that it’s you, in a context where it might not be obvious.

So in everyday conversation, you would often drop 私.

Can I change the word order, like 夏休みに私は海外旅行の計画を決めます or 私は海外旅行の計画を夏休みに決めます? Does the meaning change?

Japanese word order is somewhat flexible as long as the verb is at the end and particles remain attached to the right nouns.

These are all grammatically correct:

私は夏休みに海外旅行の計画を決めます。
夏休みに私は海外旅行の計画を決めます。
私は海外旅行の計画を夏休みに決めます。

Meaning is basically the same: you will decide the plan for an overseas trip in summer vacation.

Nuance:

Putting 夏休みに first (sentence 2) lightly emphasizes “in summer vacation”.
Moving 夏休みに closer to 決めます (sentence 3) can slightly highlight “the timing of the deciding” (i.e., I’ll decide it then, not now).

But the differences are subtle; all three are fine. Particle usage (は, に, を) is far more important than the exact order.

Can the particles に or を be dropped in casual speech here? For example, 夏休み海外旅行の計画決めます?

In very casual conversation, some particles are sometimes dropped, especially は, が, and を. But:

Dropping に from 夏休みに makes it less clear that it’s a time expression.
Dropping を from 計画を決めます is possible in very casual speech but should be avoided as a learner.

Native speakers might say (very casual):

夏休みに海外旅行の計画決める。
(drops を, keeps に)

For learners, it’s better to keep all particles:

夏休みに海外旅行の計画を決めます。

This is clear, correct, and natural.

Is this sentence natural? What are some other very natural ways a native might say almost the same thing?

The original sentence is grammatically correct and understandable:

私は夏休みに海外旅行の計画を決めます。

Some alternatives that sound very natural, depending on nuance:

Focusing on making the plan:
- 夏休みに海外旅行の計画を立てます。
  (立てる is commonly used for “making a plan”.)
Focusing on planning the trip itself:
- 夏休みに海外旅行を計画します。
Focusing on deciding to go (not just the details):
- 夏休みに海外旅行に行くことにします。
  → I will decide to go on an overseas trip in summer vacation.
Very natural and common, omitting 私:
- 夏休みに海外旅行の計画を立てます。
- 夏休みに海外旅行を計画します。

So your sentence is fine; just be aware that 計画を立てる is a very common collocation for “make a plan”.