Learn Hardcore Indonesian: Tetangga saya menanam banyak pohon kecil di depan rumah sehingga lingkungan lebih sejuk. - My neighbor plants many small trees in front of the house so the environment is cooler.

Saya tetangga would mean something like I (am) a neighbor, which changes the meaning.
Saya punya tetangga means I have a neighbor, which just states that you have neighbors, not which neighbor did the action.

In this sentence, we want my neighbor as the subject, so Tetangga saya is correct and natural.

Does saya after a noun always mean my?

Yes, when saya comes after a noun, it normally marks possession and means my:

buku saya = my book
mobil saya = my car
tetangga saya = my neighbor

When saya is used before a verb or at the start of a sentence, it’s usually the subject I:

Saya makan. = I eat / I am eating.
Saya menanam pohon. = I plant trees / I am planting trees.

So the position of saya (before a verb vs. after a noun) tells you whether it means I or my.

What is the difference between menanam and tanam here?

Tanam is the basic root verb: to plant.
Menanam is the active verb formed with the meN- prefix, and it’s what you normally use for a subject doing the action:

menanam = to plant (actively doing it)

Examples:

Tetangga saya menanam pohon. = My neighbor plants a tree / is planting a tree.
Pohon ini ditanam kemarin. = This tree was planted yesterday. (ditanam = passive)

You wouldn’t normally say Tetangga saya tanam pohon in standard Indonesian; it sounds incomplete or very colloquial. Menanam is the standard, correct form here.

Why is it banyak pohon kecil and not pohon kecil banyak?

Banyak usually comes before the noun it modifies:

banyak orang = many people
banyak masalah = many problems

So banyak pohon kecil = many small trees.

Pohon kecil banyak is possible but sounds more like:

The small trees are many (emphasizing small trees first, then saying there are many of them).

In this sentence, we’re just stating my neighbor planted many small trees, so menanam banyak pohon kecil is the natural order.

Since it says many trees, why don’t we say pohon-pohon kecil instead of pohon kecil?

Indonesian plurals are often not marked with reduplication when there is already a word showing quantity.

pohon-pohon = trees (plural, by reduplication)
banyak pohon = many trees (plural already clear from banyak)

Because banyak already tells us it’s more than one, you don’t need pohon-pohon. In fact, banyak pohon-pohon kecil usually sounds too heavy or unnatural in normal speech.

So:

banyak pohon kecil = many small trees (natural)
pohon-pohon kecil = small trees (plural emphasized, no number word)

Does di depan rumah mean in front of the house or in front of my house? Whose house is it?

Literally, di depan rumah is in front of the house (no owner marked).

However, in context, because the sentence starts with Tetangga saya (my neighbor), Indonesian speakers will often understand it as:

in front of (their / our) house in this neighborhood

If you want to be explicit:

di depan rumah saya = in front of my house
di depan rumah tetangga saya = in front of my neighbor’s house
di depan rumah kami = in front of our house

The original sentence leaves it general, which is very common and natural in Indonesian.

What does sehingga mean here, and how is it different from jadi or karena?

Sehingga is a conjunction meaning so that / as a result, introducing a result clause.

In the sentence:

… menanam banyak pohon kecil di depan rumah sehingga lingkungan lebih sejuk.
→ … planted many small trees in front of the house, so the surroundings are cooler.

Differences:

sehingga: emphasizes a result (A happens, resulting in B)
- Dia sakit sehingga tidak bisa bekerja. = He is sick, so (as a result) he can’t work.
jadi: also means so / therefore, more informal and often starts the result clause
- Dia sakit, jadi dia tidak bisa bekerja.
karena: means because, introduces a reason
- Dia tidak bisa bekerja karena dia sakit. = He can’t work because he is sick.

Here sehingga is good and fairly neutral; you could also say jadi lingkungan lebih sejuk in casual speech.

What exactly does lingkungan mean here? Is it environment, neighborhood, or something else?

Lingkungan is a flexible word. It can mean:

the environment (in a physical or ecological sense)
the surroundings / area around
the neighborhood / local area

In this sentence, lingkungan lebih sejuk suggests the surrounding area / the neighborhood feels cooler because of the trees. It doesn’t only refer to nature in a global sense; it’s about the immediate environment around the house.

Why is it lebih sejuk and not lebih dingin? What’s the difference between sejuk and dingin?

Both relate to temperature, but with different nuances:

dingin = cold (can be unpleasantly or neutrally cold)
- Airnya dingin. = The water is cold.
sejuk = cool, pleasantly cool, refreshing
- Udaranya sejuk. = The air is cool (nice, comfortable).

With lebih:

lebih dingin = colder (possibly too cold)
lebih sejuk = cooler (more pleasantly cool)

Because planting trees usually makes the air comfortably cooler, lebih sejuk fits better than lebih dingin, which could sound like too cold.

Why is there no word like “become” in lingkungan lebih sejuk? Should it be menjadi lebih sejuk?

Indonesian often does not need a verb like “to be” or “to become” in this kind of sentence.

lingkungan lebih sejuk = literally the environment more cool
→ understood as the environment is cooler / becomes cooler

You can say:

lingkungan menjadi lebih sejuk = the environment becomes cooler

That’s also correct and a bit more explicit. But it’s not necessary; lingkungan lebih sejuk is very natural and commonly used.

Is this sentence formal, informal, or neutral? Would it sound natural in conversation?

The sentence is neutral and would sound natural in both:

everyday conversation
written Indonesian (e.g., in a short article)

Nothing in it is very slangy or very formal. You might hear someone say it in normal speech, for example:

Tetangga saya menanam banyak pohon kecil di depan rumah, jadi sekarang lingkungan lebih sejuk.

Adding sekarang (now) or switching sehingga to jadi makes it a bit more conversational, but the original sentence is already perfectly fine in spoken Indonesian.

Could we change the word order, for example Di depan rumah, tetangga saya menanam banyak pohon kecil? Would that still be correct?

Yes, that word order is still grammatically correct:

Di depan rumah, tetangga saya menanam banyak pohon kecil sehingga lingkungan lebih sejuk.

Putting Di depan rumah at the beginning just changes the focus a bit, emphasizing the place first:

Di depan rumah (location)
tetangga saya menanam banyak pohon kecil (what happened there)

Both versions are natural. The original version is the more straightforward, neutral order.