syukuzitu no syoutengai ha oozei no hito de nigiyaka desu.

A natural reading is:

しゅくじつ の しょうてんがい は おおぜい の ひと で にぎやか です。

A few notes:

• 祝日 = しゅくじつ = public holiday
• 商店街 = しょうてんがい = shopping street / shopping district
• 大勢 = おおぜい = a large number of people
• 人 here is ひと
• 賑やか = にぎやか = lively, bustling

That の connects 祝日 and 商店街.

So 祝日の商店街 means something like:

• the shopping street on a holiday
• the shopping street during a public holiday
• literally, holiday’s shopping street

In English we usually do not say holiday’s shopping street, but in Japanese A の B often means B related to A.

Here, 祝日 tells you the time/context for 商店街.

In 大勢の人, the の links 大勢 and 人.

This phrase means:

• many people
• a large number of people

So:

• 大勢 = a crowd / many people
• 大勢の人 = a large number of people

This is a very common pattern:

• たくさんの本 = many books
• 多くの人 = many people
• 大勢の人 = many people

大勢 specifically refers to many people. It is mostly used for crowds or large numbers of people.

So in this sentence, 大勢の人 is very natural.

Compare:

• 大勢の人 = many people
• たくさんの人 = many people
• たくさん is broader and can be used for things as well
• 大勢 is more people-focused

You would not normally use 大勢 for objects:

• natural: たくさんの本
• unnatural: 大勢の本

So 大勢 gives a stronger sense of a crowd / lots of people gathered.

は marks 商店街 as the topic:

祝日の商店街は…
= As for the shopping street on holidays...

The sentence is making a statement about the shopping street.

So the structure is:

• 祝日の商店街 = the shopping street on holidays
• は = topic marker
• 大勢の人で賑やかです = is lively with many people

If you used が instead, the nuance would change. は is the normal choice here when describing a general situation or characteristic.

This で shows the cause/reason/means for the lively condition.

So:

大勢の人で賑やかです
means roughly
It is lively because of the many people
or
It is lively with lots of people

This is a common pattern:

• 人でいっぱいです = it is full of people
• 観光客で混んでいます = it is crowded with tourists
• 子どもたちの声で賑やかです = it is lively because of children’s voices

So the で here is not the location marker. It is closer to because of / with.

Because that would mean the many people are lively/noisy, not the shopping street is lively because of the many people.

Your sentence is about the shopping street, not directly about the people.

Compare:

• 商店街は大勢の人で賑やかです。
  = The shopping street is lively with many people.

• 大勢の人が賑やかです。
  = A lot of people are lively/noisy.

That is a different meaning.

Yes, 賑やか is a na-adjective.

Na-adjectives behave differently depending on what comes after them.

Before a noun:

• 賑やかな商店街 = a lively shopping street

At the end of a sentence:

• 商店街は賑やかです = the shopping street is lively

So you use な only when the na-adjective directly modifies a noun.

That is why:

• 賑やかな商店街 ✅
• 商店街は賑やかです ✅
• 商店街は賑やかなです ❌

賑やか means lively, bustling, animated.

Depending on context, it can sometimes also mean noisy, but in this sentence it has a positive or neutral sense:

• full of people
• active
• energetic
• bustling

So the image is that the shopping street is busy and full of life on public holidays.

Yes. In normal Japanese writing, it would usually be written without spaces:

祝日の商店街は大勢の人で賑やかです。

The spaced version is often used for learners to make the parts easier to see.

Not exactly.

• 祝日 = public holiday / national holiday
• 休日 = day off / holiday / day when you do not work

So 祝日 is more specific. It refers to official holidays on the calendar.

That matters here, because the sentence suggests a typical situation on those public holidays, when shopping streets may get crowded.

Yes, that is also natural.

祝日の商店街は人が大勢いて賑やかです。
means roughly:
The shopping street is lively because there are lots of people there on holidays.

Compared with the original:

• 大勢の人で賑やかです = more compact and descriptive
• 人が大勢いて賑やかです = more explicitly says there are many people

Both are natural, but the original sentence is neat and very common in written or textbook-style Japanese.