Во время пожара паника мешает людям действовать спокойно.

Because во время is a fixed expression meaning during, and the noun after it takes the genitive case.

So:

• пожар = fire
• пожара = of a fire / during a fire

This is why you get:

• во время урока = during the lesson
• во время войны = during the war
• во время пожара = during the fire

Also, во is used instead of в here for pronunciation reasons. Russian often uses во before certain consonant combinations to make the phrase easier to say.

Пожара is in the genitive singular.

The base form is:

• пожар = fire

After во время, Russian uses the genitive:

• во время пожара = during the fire

This is very common. If you learn во время + genitive, you can use it with many nouns.

Because паника is the thing doing the action of the verb мешает.

The structure is:

• паника мешает... = panic hinders / prevents...

So grammatically:

• паника = subject, nominative case
• мешает = verb, hinders / interferes with / prevents
• людям = the people affected, in the dative case
• действовать спокойно = to act calmly

Even though English often says panic prevents people..., Russian works very similarly here: panic is still the subject.

Людям is the dative plural of люди (people).

The verb мешать commonly works like this:

• мешать кому? = to hinder someone / get in someone’s way
• мешать кому? делать что? = to prevent someone from doing something

So:

• паника мешает людям = panic hinders people
• паника мешает людям действовать спокойно = panic prevents people from acting calmly

This is an important pattern to remember:

• мешать + dative + infinitive

Examples:

• Шум мешает мне работать. = The noise prevents me from working.
• Боль мешает ему спать. = The pain keeps him from sleeping.

Because after мешать кому-то Russian often uses an infinitive to say what action is being made difficult.

So:

• мешает людям действовать = prevents people from acting

This is similar to English prevents people from acting, except Russian does not need a word like from here. It simply uses:

• мешать + dative + infinitive

That makes действовать the action that panic interferes with.

Because спокойно is an adverb, and it describes how people act.

• действовать = to act
• спокойный = calm (adjective)
• спокойно = calmly (adverb)

So:

• действовать спокойно = to act calmly

If you said спокойно действуют, that would be a finite verb phrase meaning they act calmly, but here the sentence needs an infinitive because it depends on мешает:

• мешает людям действовать спокойно

Мешает is 3rd person singular present tense of мешать.

• я мешаю
• ты мешаешь
• он / она мешает
• мы мешаем
• вы мешаете
• они мешают

It is present tense because Russian often uses the present tense for general truths or typical situations, not only for something happening right now.

So this sentence can mean something like:

• During a fire, panic interferes with people’s ability to act calmly.

It is a general statement about what panic does in that situation.

Мешать is imperfective.

That makes sense here because the sentence describes a general process or ongoing effect, not one completed single event.

• мешать = to hinder, to interfere, to keep from
• perfective partner: often помешать

Compare:

• Паника мешает людям действовать спокойно. = Panic hinders people from acting calmly.
  (general, ongoing effect)

• Паника помешала людям действовать спокойно. = Panic prevented people from acting calmly.
  (a completed event in the past)

So yes, aspect matters: the sentence uses the imperfective because it describes a general fact.

Yes, Russian word order is flexible, but the given order is natural and clear.

This version starts with the time phrase:

• Во время пожара = during a fire

Then it gives the subject and the rest:

• паника мешает людям действовать спокойно

This is a very normal way to organize information: time/context first, then the main statement.

Other orders are possible, for example:

• Паника во время пожара мешает людям действовать спокойно.
• Людям во время пожара паника мешает действовать спокойно.

These can sound slightly different in emphasis, but the original sentence is neutral and natural.

Yes, you often can, but there is a slight difference in tone and nuance.

• во время пожара = during the fire
• при пожаре = in case of fire / in a fire situation / during a fire

При пожаре is very common in instructions, safety notices, and general rules:

• При пожаре звоните 101. = In case of fire, call 101.

Во время пожара sounds a bit more like describing what happens while the fire is happening.

So in your sentence:

• Во время пожара паника мешает людям действовать спокойно.
  sounds very natural for describing behavior during an actual fire.

• При пожаре паника мешает людям действовать спокойно.
  is also possible, especially in a more general or instructional style.

Because люди is the nominative plural form, but this sentence needs the dative plural after мешать.

Forms of люди include:

• люди = people (nominative)
• людей = of people / people (accusative/genitive in many contexts)
• людям = to people
• людьми = with people
• о людях = about people

Since мешать takes the person affected in the dative, you need:

• мешает людям

not

• мешает люди

Usually yes, but in Russian паника often strongly suggests mass fear, confusion, loss of control, especially in dangerous situations.

In this sentence it means more than just being scared. It suggests a state that makes organized, calm action difficult.

That is why it fits very well with:

• мешает людям действовать спокойно

So the idea is not just people feel fear, but panic disrupts calm and effective behavior.