Мы дали козе немного сена, а овце — немного овса.

Because after дать (to give), the person or animal receiving something usually goes in the dative case.

• коза → козе = to the goat
• овца → овце = to the sheep

So the pattern is:

• Мы дали кому? — козе, овце
• We gave to whom? — to the goat, to the sheep

This is very common with verbs like дать, помочь, сказать, показать, and others that involve a recipient.

Because they come after немного, and немного normally requires the genitive case.

So:

• сено → сена
• овёс → овса

In Russian, words like много, мало, немного, сколько are typically followed by a noun in the genitive:

• немного воды = a little water
• много хлеба = a lot of bread
• немного сена = a little hay
• немного овса = a little oats

Since сено and овёс are treated as mass nouns here, Russian uses the genitive singular.

Yes, normally the thing given is the direct object, and direct objects are often in the accusative. But here the direct object is not just сено or овёс by themselves. The direct object is the whole quantity phrase:

• немного сена
• немного овса

With quantity words like немного, the noun inside that phrase goes into the genitive. So the whole phrase functions as the object of дали.

You can think of it like this:

• дали [немного сена]
• gave [a little hay]

The object is the full phrase, not just the noun alone.

Дали is the perfective past of дать, and it shows a completed action: they gave the hay and oats, and that action is presented as a finished event.

• дали = gave, in a completed sense
• давали = were giving / used to give / gave repeatedly

In this sentence, the speaker is talking about one completed act, so дали is the natural choice.

Also, дали is plural because the subject is мы (we).

Here а introduces a contrast or comparison between the two parts:

• козе немного сена
• а овце — немного овса

It is not a strong but, but it is more contrastive than plain and. In English, depending on context, it can sound like:

• and
• while
• whereas
• and as for...

So the sentence has the feeling of:

• We gave the goat a little hay, and the sheep a little oats.
• We gave the goat a little hay, while the sheep got a little oats.

Using и would sound less contrastive and less neatly paired.

The dash shows that something has been left out because it is understood. The omitted word is the verb дали.

Full version:

• Мы дали козе немного сена, а овце дали немного овса.

Russian often omits repeated words when they are obvious, especially in parallel structures. The dash helps mark that omission clearly:

• а овце — немного овса

So the dash here is basically signaling:

• and to the sheep — [we gave] a little oats

Yes. Russian word order is fairly flexible because the cases show the grammatical roles.

The sentence as written is natural and balanced:

• Мы дали козе немного сена, а овце — немного овса.

But other orders are possible, for example to shift emphasis:

• Козе мы дали немного сена, а овце — немного овса.
• Немного сена мы дали козе, а немного овса — овце.

These versions are still grammatical, but they sound different in focus. The original version is a very neutral, natural way to say it.

A natural stressed version is:

Мы да́ли козе́ немно́го се́на, а овце́ — немно́го овса́.

A few useful points:

• дали → stress on да́-
• козе → stress on the last syllable: козе́
• немного → stress on -но́-
• сена → stress on се́-
• овце → stress on the last syllable: овце́
• овса → stress on the last syllable: овса́

Also, овёс in dictionary form has ё, which is always stressed: овёс. But in this sentence the form is овса́, where the stress moves.

It is a normal inflection pattern for this word, but it can feel surprising at first because the stressed ё disappears in other forms.

The forms are:

• nominative: овёс
• genitive: овса
• dative: овсу
• instrumental: овсом
• prepositional: об овсе

So in the sentence, after немного, you need the genitive form овса.

This kind of vowel/stress change is not unusual in Russian. It is something learners usually just memorize together with the noun.

Here немного means a little, some, or not much in the sense of a small quantity.

So:

• немного сена = a little hay
• немного овса = a little oats

It is written as one word because it is the normal quantity word немного.

Russian also has не много as two words, but that usually appears in a true negation or contrast, for example:

• Не много, а мало. = Not much, but little.

In your sentence, it is the ordinary quantity expression, so немного is written together.

Овце here is singular.

The dictionary form is овца = a sheep / ewe.
In this sentence, it becomes dative singular:

• овца → овце = to the sheep

That can be tricky for English speakers because sheep does not change between singular and plural in English, but Russian does distinguish them clearly.

For comparison:

• singular nominative: овца
• singular dative: овце
• plural nominative: овцы
• plural dative: овцам