Learn Hardcore Indonesian: Pagi ini kami berjalan di ladang pertanian di desa kakek. - This morning we walk in the agricultural field in my grandfather’s village.

Putting ini after the time word is the normal pattern.
Ini pagi is not natural Indonesian for this morning and would sound wrong or at least very odd in this context.

So:

Pagi ini kami berjalan ... = This morning we walked ...
Hari ini kami berjalan ... = Today we walked ...

Does the sentence mean “This morning we walked” (past) or “This morning we are walking” (present)? There’s no tense marker.

Indonesian verbs do not change form for tense. Berjalan can mean:

walk / are walking / were walking / walked, depending on context.

In Pagi ini kami berjalan di ladang pertanian di desa kakek, the time phrase pagi ini (this morning) tells us when it happens, but not clearly whether it is:

already finished (earlier this morning),
happening right now (it is this morning), or
planned for this morning.

To be more explicit, Indonesian can add other words:

Tadi pagi kami berjalan ... = This morning / earlier this morning we walked ... (definitely past, earlier today)
Pagi ini kami sedang berjalan ... = This morning we are walking ... (ongoing right now)
Pagi ini kami akan berjalan ... = This morning we will walk ... (future, planned)

So the original sentence is tense‑neutral; context decides how you translate it in English.

Why is kami used instead of kita? Aren’t both “we”?

Both kami and kita mean we, but they differ in whether they include the person you’re talking to:

kami = we (*not including the listener*)
kita = we (*including the listener*)

In this sentence:

Pagi ini kami berjalan ... ≈ This morning *we (but not you) walked ...*

If the speaker wants to include the listener, they would say:

Pagi ini kita berjalan di ladang pertanian di desa kakek.
= This morning *you and I (and maybe others) walked in the farmland in Grandfather’s village.*

So the original sentence implies the listener was not part of the group.

What exactly does berjalan mean here? Could I also say jalan or berjalan-jalan?

The root is jalan (road / to walk). Common forms:

berjalan – to walk (fairly neutral, a bit more formal)
jalan – to walk (very common in casual speech)
jalan-jalan – to stroll / to go for a walk / to wander around for leisure

In your sentence:

Pagi ini kami berjalan di ladang pertanian ...
= We walked / were walking (neutral).

You could also say:

Pagi ini kami jalan di ladang pertanian ...
– natural in everyday spoken Indonesian.

If you want to emphasize that it was a leisurely walk / sightseeing, you can say:

Pagi ini kami jalan-jalan di ladang pertanian di desa kakek.
= This morning we went for a walk / strolled around the farmland in Grandfather’s village.

Why do we use di before ladang pertanian? What’s the difference between di and ke?

di and ke are different prepositions:

di = in / at / on (location, where something is)
ke = to / towards (direction, where something is going)

In your sentence:

di ladang pertanian = in the farmland (location)

So:

Kami berjalan di ladang pertanian
= We walked in the farmland.

If you say:

Kami berjalan ke ladang pertanian
= We walked to the farmland (the farmland is the destination, not the area where they walked around).

So di is correct here because the walking happens inside or within the farmland.

What does ladang pertanian mean exactly? How is it different from sawah or kebun?

Some useful words for land used for growing things:

ladang – dry field, usually for seasonal crops (corn, cassava, etc.), not flooded.
sawah – rice paddy field, usually wet/flooded for growing rice.
kebun – garden/orchard/plantation (for fruit trees, vegetables, tea, coffee, etc.).
pertanian – agriculture / farming (a noun, or used as an adjective: agricultural).

Ladang pertanian literally means agricultural fields / farmland.
It can sound slightly redundant (since ladang already implies farming), but it can be used to emphasize that these are farmlands, not just any kind of open land.

You could also say:

di ladang – in the fields (dry fields)
di sawah – in the rice fields
di kebun – in the garden/orchard

The exact word you choose depends on what kind of land you’re talking about.

How does desa kakek express “grandfather’s village”? There is no word like “of” or “’s”.

Indonesian often shows possession simply by putting two nouns next to each other, usually:

[thing] + [owner/person]

For example:

rumah ibu = mother’s house
buku Ali = Ali’s book
desa kakek = grandfather’s village

So desa kakek naturally means “the village associated with Grandfather” (usually interpreted as Grandfather’s village).

If you want to make it very clear that this is my grandfather, you can add a pronoun:

desa kakek saya = my grandfather’s village
desa kakekku = my grandfather’s village (more informal, with the suffix -ku = my)

Without saya / -ku, desa kakek could be my grandfather, your grandfather, or someone’s grandfather; context clarifies whose.

Why do we have di twice: di ladang pertanian di desa kakek? Is that necessary?

In the sentence:

... berjalan di ladang pertanian di desa kakek.

there are two location phrases:

di ladang pertanian – in the farmland
di desa kakek – in Grandfather’s village

Together, they give a more precise location:

We walked in the farmland (which is) in Grandfather’s village.

Using di twice is completely normal when you stack locations like this.

You could slightly rephrase:

di ladang pertanian desa kakek
(farmland of Grandfather’s village)

But the original with di ... di ... is very natural and clear.

Can I move pagi ini to the end and say: Kami berjalan di ladang pertanian di desa kakek pagi ini?

Yes. Indonesian word order for time expressions is quite flexible.

Both are correct:

Pagi ini kami berjalan di ladang pertanian di desa kakek.
Kami berjalan di ladang pertanian di desa kakek pagi ini.

Putting pagi ini at the beginning often gives it a little more emphasis, like setting the scene:

Pagi ini, (as for this morning), we walked in the farmland ...

At the end, it sounds more like an extra piece of information:

We walked in the farmland in Grandfather’s village this morning.

If I want to say clearly “we are walking (right now) this morning in the farmland”, how can I show that progressive meaning in Indonesian?

To show that an action is ongoing / in progress, Indonesian often uses sedang before the verb.

You can say:

Pagi ini kami sedang berjalan di ladang pertanian di desa kakek.
= This morning we are walking in the farmland in Grandfather’s village.

You can also put sedang slightly later:

Pagi ini kami sedang berjalan di ladang pertanian di desa kakek. (most natural)
Kami sedang berjalan di ladang pertanian di desa kakek pagi ini. (also fine)

Without sedang, kami berjalan is more neutral and can be translated as walk / walked / are walking, depending on context.