niwa ni tiisai koya ga aru.

に marks the location where something exists.

In this sentence:

• 庭に = in the garden
• 小屋がある = there is a hut

So に is telling you the place in which the hut exists.

A useful pattern is:

• Place に Thing が ある
• Place に Person/Animal が いる

So this sentence follows a very common existence pattern in Japanese.

が marks the thing that exists: the hut.

In 小屋がある, the hut is the thing being identified as existing. So が is very natural here.

Compare:

• 小屋がある = there is a hut
• 小屋はある = as for the hut, it exists / there is a hut, at least

Using が is the neutral, standard choice when you are simply stating that something is there.

Japanese uses different existence verbs depending on whether the thing is animate or inanimate.

• ある = used for things, objects, places, plants, etc.
• いる = used for people and animals

A hut is an inanimate object, so ある is correct.

Examples:

• 庭に小屋がある。 = There is a hut in the garden.
• 庭に犬がいる。 = There is a dog in the garden.

Because Japanese adjectives usually come before the noun they describe, just like in English.

• 小さい小屋 = small hut

Here, 小さい is an い-adjective, and it directly modifies 小屋.

This is a very common pattern:

• 大きい家 = big house
• 古い車 = old car
• 静かな部屋 = quiet room

So 小さい小屋 is completely normal structurally.

Yes. Both are possible, but they are a little different in feel.

• 小さい小屋 = straightforward, ordinary small hut
• 小さな小屋 = often sounds a bit more descriptive, literary, or emotionally colored

In everyday speech, 小さい小屋 is very common and completely correct.
You may also see 小さな小屋, especially in written or more expressive language.

So for a learner, it is best to understand that:

• 小さい is the regular adjective form
• 小さな is a special noun-modifying form of 小さい

Japanese does not have articles like a, an, or the.

So 小屋 can mean:

• a hut
• the hut

Which one is meant depends on context.

In an out-of-the-blue sentence like this, English usually translates it as a small hut because it sounds like new information being introduced.

Japanese and English organize this idea differently.

English often says:

• There is a small hut in the garden.

Japanese literally follows something closer to:

• In the garden, a small hut exists.

So:

• 庭に = in the garden
• 小さい小屋が = a small hut
• ある = exists / there is

Japanese relies heavily on particles like に and が, so word order is more flexible than in English, though this order is very natural.

Because ある is already the verb, and it can end a sentence by itself.

This sentence is in plain form:

• 庭に小さい小屋がある。

A polite version would be:

• 庭に小さい小屋があります。

You do not add です after ある here.

So:

• plain: ある
• polite: あります

Yes, but the nuance changes.

• 庭に小さい小屋がある。
  = There is a small hut in the garden.
  This simply states the existence of the hut.

• 庭に小さい小屋はある。
  = There is at least a small hut in the garden / As for a small hut, there is one.
  This sounds contrastive or emphatic.

Also possible:

• 庭には小さい小屋がある。
  = In the garden, there is a small hut.
  This can sound like as for the garden...

So が is the most neutral choice for a simple existence statement.

Yes, the order can sometimes be changed because particles show the role of each word.

The most basic and natural order here is:

• 庭に小さい小屋がある。

You may also see variations such as:

• 小さい小屋が庭にある。

Both are grammatical, but the emphasis may shift slightly.

• 庭に... first makes the location the starting point
• 小さい小屋が... first puts more focus on the hut

For learners, the original order is a very good standard pattern to remember.

Not perfectly, but hut is a good translation.

小屋 usually refers to a small building or shed-like structure. Depending on context, it could be:

• a hut
• a shed
• a small cabin
• a shack

So the exact English word depends on what kind of 小屋 it is. But for learning this sentence, hut is a reasonable translation.

Yes, it is natural and grammatically correct.

A native speaker might also say:

• 庭に小さな小屋がある。
• 庭に小屋がある。
• 庭には小さい小屋がある。

But 庭に小さい小屋がある。 is a normal sentence and a good example of the pattern:

• Place に
• Thing が
• ある

So it is a very useful model sentence for beginners.