ekimae no hiroba no hunsui no mawari ni, kankou de kita hito ga takusan atumatte imasita.

A useful way is to work from right to left.

• 周り = the area around / surroundings
• 噴水の周り = the area around the fountain
• 広場の噴水の周り = the area around the fountain in the plaza
• 駅前の広場の噴水の周り = the area around the fountain in the plaza in front of the station

In Japanese, の often links nouns together, and each earlier noun modifies the noun after it.

They are very close, but not exactly identical in feel.

• 駅の前 = literally in front of the station
• 駅前 = the station-front area; a very common set expression

So 駅前の広場 feels like the plaza in the station-front area or simply the plaza in front of the station.
Japanese often uses compact words like 駅前, 店内, 校内, etc. where English would use a longer phrase.

周り is a noun, not a preposition.

That is why it works like this:

• 噴水の周り = the area around the fountain
• 噴水の周りに = around the fountain / in the area around the fountain

This is very common in Japanese. Words that English treats like prepositions are often nouns in Japanese:

• 上 = top / above
• 下 = bottom / below
• 前 = front / before
• 後ろ = back / behind
• 周り = surroundings / around

Because 集まる often uses に for the place or point that people gather to / around.

• 駅に集まる = gather at the station
• 噴水の周りに集まる = gather around the fountain

Here, に marks the location where the people ended up gathering.

If you used で, it would sound more like emphasizing the place where the action happens in a general sense. With 周り, に is the more natural choice for gather around X.

A good comparison:

• 広場で集まる = gather in the plaza
• 噴水の周りに集まる = gather around the fountain

観光で来た人 means people who came for sightseeing or people who came as tourists.

Here, で marks the reason/background/circumstance for coming.

This is a common pattern:

• 仕事で来た = came for work
• 旅行で来た = came on a trip
• 観光で来た = came for sightseeing

So 観光で来た人 is literally people who came because of sightseeing / for tourism purposes.

Yes, absolutely. 観光に来た人 is also natural and very common.

The difference is small:

• 観光に来た人 = people who came to sightsee
• 観光で来た人 = people who came for sightseeing / as tourists

You can think of に as marking purpose more directly, while で often gives a reason/background flavor. In real life, both can be used, and the difference is often subtle.

Because the coming happened before the gathering.

• 来た人 = people who came / have come
• 来る人 = people who come / are coming / will come, depending on context

In this sentence, the people are already there, gathered around the fountain. So the action come is already completed from that viewpoint, which is why 来た人 is natural.

Because Japanese uses a relative clause directly before the noun, with no need for who, that, or which.

So:

• 観光で来た人 = the people who came for sightseeing
• 昨日会った先生 = the teacher I met yesterday
• 私が読んだ本 = the book I read

This is one of the biggest structural differences from English:

• English: the people who came
• Japanese: came people → 来た人

Because が marks the subject of 集まっていました.

Here, the sentence is simply saying that people gathered there. が is natural for introducing or identifying the subject in this kind of description.

• 観光で来た人がたくさん集まっていました = many people who had come for sightseeing were gathered there

If you used は, it would feel more like setting up a topic or contrast:

• 観光で来た人はたくさん集まっていました
  • As for the people who came for sightseeing, many had gathered...

That is possible in some contexts, but が is more neutral and straightforward here.

In meaning, it gives the quantity of the people: many people gathered.

Japanese often uses たくさん in an adverb-like position before the verb:

• 人がたくさん集まる = many people gather

You can also say:

• たくさんの人が集まる

Both mean roughly the same thing.

So in this sentence:

• 人がたくさん集まっていました = many people were gathered / had gathered

Even though たくさん sits near the verb, the natural English meaning is about the number of people.

集まっていました gives more of a scene description.

With ～ていました, this can mean:

• an action in progress, or
• a resulting state in the past

Here it most naturally suggests a past scene: people were gathered around the fountain.

So:

• 集まりました = gathered
• 集まっていました = were gathered / had gathered and were there

This fits the image of someone describing what the area looked like at that time.

集まる is intransitive: to gather / assemble
集める is transitive: to gather / collect something

Examples:

• 人が集まる = people gather
• 人を集める = gather people
• 切手を集める = collect stamps

In your sentence, the people themselves are gathering, so 集まる is the correct verb.