Справедливость очень важна в дружбе.

Because it agrees with справедливость, which is a feminine noun in Russian.

• справедливость = fairness / justice
• It ends in -ость, and nouns of this type are usually feminine.
• In sentences like this, the short-form adjective agrees with the subject:

So:

• справедливость важна = fairness is important
  not
• справедливость важный

Here, важна is the short feminine singular form of важный.

In Russian, the verb to be is usually omitted in the present tense.

So:

• Справедливость очень важна в дружбе. literally looks like
• Fairness very important in friendship.

But it naturally means:

• Fairness is very important in friendship.

This is completely normal in Russian. In the present tense, you usually do not say есть to mean is in sentences like this.

It can mean fairness, justice, or a sense of what is fair, depending on context.

In this sentence, fairness is usually the best translation, because friendship is a personal relationship, and the idea is probably that being fair to each other matters.

So although справедливость can sometimes sound more abstract or philosophical, here it most naturally means something like:

• fairness
• being fair
• a sense of justice/fairness

Because очень means very, and it normally goes before the adjective or adverb it modifies.

So:

• очень важна = very important

This is similar to English word order:

• very important

You would not normally put очень after важна here.

Дружбе is in the prepositional case because it follows the preposition в here.

• дружба = friendship
• в дружбе = in friendship

The noun changes like this:

• nominative: дружба
• prepositional: в дружбе

So the phrase means in friendship or when it comes to friendship.

Literally, it is in friendship, but in natural English you would often translate it as:

• in friendship
• in a friendship
• in friendships
• when it comes to friendship

Russian often uses singular abstract nouns where English may choose a more flexible wording.

So в дружбе is not necessarily talking about one specific friendship. It can mean friendship as a general concept.

Yes, but the meaning and style are different.

In this sentence, важна is the short form, which is very commonly used in statements like:

• X важен / важна / важно = X is important

So:

• Справедливость очень важна. = Fairness is very important.

If you used важная, that would usually be the full form, and full-form adjectives are more commonly used:

• before a noun: важная вещь = an important thing
• or in some predicate uses with a slightly different feel

For a simple statement like Fairness is important, the short form важна is the normal choice.

Yes, that is possible.

Russian word order is more flexible than English, because case endings carry a lot of the grammatical meaning.

Both of these are correct:

• Справедливость очень важна в дружбе.
• В дружбе справедливость очень важна.

The difference is mainly focus:

• Справедливость очень важна в дружбе.
  starts with fairness as the topic
• В дружбе справедливость очень важна.
  emphasizes the context in friendship

So the original sentence is neutral and natural, but the alternative is also good.

Russian has no articles.

So Russian does not directly mark the difference between:

• fairness
• the fairness
• a fairness (though this one is unusual in English anyway)

Likewise, дружбе does not show a friendship vs the friendship through an article. You understand that from context.

That is why Russian learners of English must learn to add articles, while English speakers learning Russian must get used to leaving them out.

Because в can mean either in or into, depending on the case that follows.

• в + prepositional usually means in
• в + accusative often means into

Here we have:

• в дружбе

And дружбе is prepositional, so the meaning is in friendship, not into friendship.

It sounds natural and neutral, but a little thoughtful or generalizing because it talks about an abstract idea.

• справедливость is an abstract noun
• в дружбе is also a general statement

So it sounds like something you might hear in:

• advice
• discussion of values
• a textbook
• an essay
• thoughtful conversation

It does not sound strange or unnatural. It is a normal Russian sentence.

Yes, that is also possible, but the meaning shifts a little.

• в дружбе = in friendship, within the relationship itself
• для дружбы = for friendship, for the existence or success of friendship

So:

• Справедливость очень важна в дружбе.
  = fairness is important within friendship
• Справедливость очень важна для дружбы.
  = fairness is important for friendship to work or survive

They are close in meaning, but в дружбе focuses more on the setting, while для дружбы focuses more on what friendship needs.