На ферме дети обнимают друг друга, когда видят маленьких кроликов.

In Russian, ферма is normally used with на when you mean being at the farm / on the farm as a place of activity.

So:

• на ферме = at/on the farm
• на ферму = to the farm (movement toward it)

Using в ферме here would sound unnatural, because it suggests being physically inside something called a farm, rather than simply being at the farm.

Also, ферме is in the prepositional case because it follows на in a location meaning.

Because когда видят маленьких кроликов is a subordinate clause.

Russian normally puts a comma before conjunctions like когда, если, потому что, and so on when they introduce a dependent clause.

So the sentence is divided like this:

На ферме дети обнимают друг друга, когда видят маленьких кроликов.

Main clause: На ферме дети обнимают друг друга

Subordinate clause: когда видят маленьких кроликов

In Russian, that comma is required.

The subject is understood to be the same as in the main clause: дети.

Russian often leaves out a repeated subject when it is already clear from context. So:

• когда видят маленьких кроликов = when they see little rabbits
• the they is understood to mean the children

You could say когда они видят маленьких кроликов, but it is often unnecessary because видят already shows 3rd person plural, and the subject is obvious.

Here the present tense expresses a general or habitual action, not necessarily something happening only right now.

So the sentence means something like:

• The children hug each other when/whenever they see little rabbits.

This is a common use of the Russian present tense: it can describe what people usually do.

Both verbs are also imperfective:

• обнимать → обнимают
• видеть → видят

That fits well because the sentence describes a repeated pattern, not one completed event.

In this sentence, когда can naturally have the sense of when or whenever, because the whole sentence is in a habitual/general present.

So:

• когда видят маленьких кроликов can be understood as when they see little rabbits
• but in natural English the idea is often closer to whenever they see little rabbits

Russian does not need a separate word here to create that whenever meaning; the context and tense already do that.

Yes, обнимаются is also possible.

Both can mean that the children hug one another, but there is a small difference in feel:

• обнимают друг друга = explicitly hug each other
• обнимаются = are hugging / hug one another, with the mutual meaning built into the verb

The version with друг друга is very clear for a learner because it directly shows the idea of each other.

So:

• Дети обнимают друг друга = correct
• Дети обнимаются = also correct

Друг друга is the standard Russian way to say each other.

It is a fixed reciprocal expression. In practice, you learn it as a set phrase.

In this sentence, it is the object of обнимают, so it is in the accusative:

• обнимать кого? → друг друга

A useful thing to know is that the second word changes depending on the case:

• друг друга = each other (accusative/genitive form)
• друг другу = to each other
• друг другом = with each other
• друг о друге = about each other

Even though друг by itself means friend, in this expression друг друга simply means each other and should be understood as one unit.

Because маленьких кроликов is the direct object of видят.

The verb видеть takes the accusative case:

• видят кого? что? → маленьких кроликов

Now the important part: кролики are animate, and in Russian the accusative plural of animate nouns looks the same as the genitive plural.

That is why you get:

• кролики = nominative plural
• кроликов = accusative plural for animate nouns

The adjective matches the noun:

• маленькие кролики = nominative plural
• маленьких кроликов = accusative plural animate

So even though it looks like genitive, here it is functioning as accusative.

Yes, you could.

Russian word order is more flexible than English word order. The version in the sentence starts with На ферме to set the scene first:

• На ферме дети обнимают друг друга... = On the farm, the children hug each other...

But other orders are also possible, for example:

• Дети на ферме обнимают друг друга...

That version is still grammatical, but the emphasis is a little different. Starting with На ферме highlights the location first.

So the word order in the original sentence is natural, but not the only possible one.