Learn Hardcore Indonesian: Anjing saya bermain dengan rantai di halaman belakang. - My dog plays with a chain in the backyard.

In Indonesian, possessive pronouns usually come after the noun they modify.
So anjing saya literally means dog I, but it is understood as my dog.
Other examples: rumah saya (my house), ibu saya (my mother), teman saya (my friend).
Putting saya before the noun (saya anjing) would sound like "I am a dog", not "my dog".

Can I also say Anjingku bermain dengan rantai di halaman belakang? What is the difference between anjing saya and anjingku?

Yes, Anjingku is correct and means the same thing as anjing saya: my dog.
-ku is a possessive suffix attached directly to the noun (anjing + -ku).
Anjing saya sounds a bit more neutral or formal; anjingku is more informal and can feel a bit more personal or intimate.
In everyday speech, Indonesians very commonly use both patterns.

Why is there no word for a or the in this sentence?

Indonesian does not use articles like a/an or the.
Whether you mean a dog or the dog is understood from context, not from a specific word.
So anjing saya can mean my dog (the specific one you own) or just my dog in a general sense, depending on the situation.
If you really need to emphasize that specific one, you might use other structures or context, but there is still no direct equivalent of the.

What exactly does dengan do in bermain dengan rantai? Does it mean with like together with, or using?

Dengan is a very flexible word that usually translates as with.
Here, bermain dengan rantai means playing with a chain, in the sense of interacting with it (biting it, pulling it, etc.).
In other contexts, dengan can also mean using something: menulis dengan pensil (to write with a pencil).
So in this sentence it combines both ideas: the dog is playing and the chain is the object used/played with.

Can rantai also mean leash, or only chain?

The basic meaning of rantai is chain—typically made of metal links.
A leash is usually called tali (rope/cord) or tali anjing (dog leash).
If the leash is literally made of metal chain, a speaker might still say rantai anjing, but rantai itself does not automatically mean leash.

Why is di halaman belakang placed at the end of the sentence? Could I move it somewhere else?

Indonesian word order is fairly flexible, especially for information like place and time.
Anjing saya bermain dengan rantai di halaman belakang is very natural, with the place coming last.
You could say Di halaman belakang, anjing saya bermain dengan rantai, especially if you want to emphasize in the backyard.
Both are grammatically correct; putting the location at the end is the most neutral, everyday pattern.

What is the difference between halaman belakang and belakang rumah for backyard?

Halaman belakang literally means back yard (yard at the back).
Halaman is yard / yard area (often the open space around a house), and belakang is back.
Belakang rumah literally means the back of the house and can refer more to the back area, not necessarily a yard with grass or open space.
In practice, halaman belakang is the closest to backyard.

How do I say that the dog was playing, not is playing? There is no past tense marker in bermain.

Indonesian verbs don’t change form for tense. Bermain can mean plays, is playing, or played, depending on context.
To make the time clear, Indonesians add time expressions like tadi (earlier), kemarin (yesterday), sekarang (now), etc.
For example: Tadi anjing saya bermain dengan rantai di halaman belakang clearly means earlier, my dog was playing with a chain in the backyard.

Can I drop dengan and say Anjing saya bermain rantai di halaman belakang?

No, that sounds wrong in Indonesian.
Bermain is normally intransitive (it does not take a direct object) when it means to play.
To show what you play with, you use dengan: bermain dengan bola, bermain dengan teman, bermain dengan rantai.
Without dengan, bermain rantai is ungrammatical or at best very odd.

Is bermain only used for children and animals, or can adults also bermain?

Adults can definitely bermain too.
You can say bermain bola (play ball/soccer), bermain gitar (play the guitar), bermain kartu (play cards), etc., regardless of age.
In casual speech, people often shorten bermain to main: Anjing saya main dengan rantai di halaman belakang (very common in conversation).
Both bermain and main are acceptable; bermain is just a bit more formal/complete.

Why do we use di before halaman belakang? Could we use ke, pada, or dalam instead?

Di is the standard preposition for a static location: at / in / on.
Di halaman belakang means in the backyard / at the backyard area.
Ke halaman belakang would mean to the backyard (movement toward it).
Dalam halaman belakang is usually not used; dalam is more like inside (something enclosed).
Pada is more formal and often used with abstract nouns or time; it would sound odd here.

If I want to say in the backyard with a more definite feel, can I say di halaman belakangnya?

Yes, di halaman belakangnya is possible and it adds a sense of that particular backyard or his/her/their/its backyard, depending on context.
The suffix -nya can work like the, or like his/her/its/their, but it’s context-dependent.
Without -nya, di halaman belakang is already natural and usually enough.
You would add -nya only if the context strongly points to a specific, already-known backyard (for example, di halaman belakangnya rumah itu – in the backyard of that house).