Право ответа получила команда знатоков.

Because Право ответа is not the subject here. The subject is команда знатоков.

In Russian, word order is flexible, so the sentence does not have to begin with the subject. The verb agrees with the noun in the nominative case, and here that is команда.

So:

• Право ответа = the object, in the accusative
• команда знатоков = the subject, in the nominative
• получила = feminine singular, agreeing with команда

A more neutral word order would be:

Команда знатоков получила право ответа.

Same basic meaning, but less emphasis on право ответа.

Here is the breakdown:

• Право — accusative singular
  It is the direct object of получила.
  Since право is a neuter inanimate noun, its accusative form is the same as the nominative.

• ответа — genitive singular
  It depends on право in the expression право ответа.

• получила — past tense, feminine singular of получить

• команда — nominative singular
  This is the subject of the sentence.

• знатоков — genitive plural
  It depends on команда and means of experts / of connoisseurs / of the knowledgeable players, depending on context.

So literally the structure is something like:

[The right of answering] received [the team of experts]

But grammatically it means:

The team of experts got the right to answer.

Because after право in this meaning, Russian often uses the genitive case.

So:

• право голоса = the right to vote / voting rights
• право выбора = the right to choose
• право ответа = the right to answer / right of reply

The noun after право names the action or sphere the right concerns, and that noun is commonly put in the genitive.

So ответа is not random—it is the normal pattern here.

Because команда знатоков means a team of experts.

In Russian, when one noun describes the members or contents of a group, the second noun is often put in the genitive:

• группа студентов = a group of students
• команда игроков = a team of players
• отряд солдат = a detachment of soldiers
• команда знатоков = a team of experts

So:

• команда = team
• знатоков = of experts

Also, знатоков is plural because the team contains more than one expert.

Because the grammatical subject is команда, and команда is:

• singular
• feminine

So the verb must also be:

• singular
• feminine past

That gives получила.

Even though a team consists of many people, Russian usually treats команда as one unit, just like English often does with the team got.

So:

• команда получила = correct standard agreement

Using получили would shift the subject to the people themselves, not the noun команда. With команда, singular agreement is the normal choice.

Получить is a perfective verb. In the past tense, получила presents the action as a completed event:

the team got / received the right to answer

That fits the context well, because receiving the right is a single completed moment.

Compare:

• получила = received, got
• получала = was receiving / used to receive / received repeatedly

In this sentence, the perfective form tells us that the right was granted at a particular moment.

Yes. Russian word order often helps show topic and focus.

Compare:

• Команда знатоков получила право ответа.
  Neutral: The team of experts received the right to answer.

• Право ответа получила команда знатоков.
  More emphasis on право ответа or on who got it.

This order can sound a bit more dramatic or formal, as if the important point is:

As for the right to answer, it was the experts’ team that got it.

So the fronted object is not wrong or strange—it is a meaningful stylistic choice.

It means the right to answer.

Depending on context, it can also be translated more naturally as:

• the right to respond
• the chance to answer
• the floor to answer
• the right of reply in more formal or media-related contexts

In a quiz or game-show context, право ответа often means that this team is now allowed to give the answer.

Yes, absolutely. That is probably the most neutral word order.

So both are correct:

• Команда знатоков получила право ответа.
• Право ответа получила команда знатоков.

The difference is mainly emphasis and style, not basic grammar.

The first is straightforward and neutral.
The second highlights право ответа and sounds a bit more marked.

Because Russian has no articles.

Russian does not have separate words for a/an and the. Whether something is definite or indefinite is understood from:

• context
• word order
• intonation
• the situation

So команда знатоков can mean:

• a team of experts
• the team of experts

and право ответа can mean:

• a right to answer
• the right to answer

In real context, the intended meaning is usually clear.