На пикнике мы будем жарить сосиски на огне.

Because на is commonly used with events and activities to mean at or during them.

• на пикнике = at the picnic
• The noun пикник changes to the prepositional case after на when it means location or setting.
• So:
  • пикник → dictionary form
  • на пикнике = at a picnic / at the picnic

This is similar to:

• на концерте = at the concert
• на уроке = in class / at the lesson
• на работе = at work

Мы будем жарить is the future tense.

Russian often forms the future of an imperfective verb by using:

• будем
  • infinitive

Here:

• будем = we will
• жарить = to fry / grill / roast

So:

• мы будем жарить = we will be grilling / we will grill

By contrast:

• мы жарим usually means we are grilling or sometimes we grill depending on context, but not normally a clear future.

Yes. Russian has two common ways to talk about the future, depending on aspect.

1. Imperfective future: будем + infinitive

   • будем жарить
   • focuses on the process, activity, or repeated action

2. Perfective future: one verb form

   • пожарим
   • focuses more on the action as a completed result

So:

• Мы будем жарить сосиски = We’ll be grilling sausages / We’ll grill sausages
  Emphasis: the activity itself

• Мы пожарим сосиски = We’ll grill/cook the sausages
  Emphasis: getting them cooked

In this picnic sentence, будем жарить sounds very natural because it describes what people will be doing at the picnic.

Here жарить means something like:

• to fry
• to roast
• to grill

In the sentence на огне makes the meaning closer to grill/roast over a fire.

So жарить сосиски на огне is essentially:

• to grill sausages over a fire

It is a broad verb, and the exact English translation depends on context.

Сосиски is the accusative plural of сосиска.

• singular: сосиска = sausage
• plural: сосиски = sausages

It is in the accusative because it is the direct object of жарить:

• What will we grill?
• сосиски

For inanimate plural nouns, the accusative plural usually looks the same as the nominative plural.

So:

• nominative plural: сосиски
• accusative plural: сосиски

That is why the form does not change here.

На огне literally means on the fire, but in natural English it usually means:

• over the fire
• on an open fire

Again, на is followed by the prepositional case here:

• огонь → огне

This is a set phrase used for cooking:

• готовить на огне = cook over a fire
• жарить на огне = grill/roast over a fire

So although the literal wording is on the fire, the real meaning is over the fire.

Yes, it could be omitted.

Russian often leaves out subject pronouns when they are clear from the verb ending.

• Будем жарить сосиски на огне. = We will grill sausages over the fire.
• Мы будем жарить сосиски на огне. = We will grill sausages over the fire.

Including мы can:

• add emphasis
• make the subject explicit
• sound a little more contrastive, like we will do it

So both are possible, but мы is not always necessary.

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

The neutral order here is:

• На пикнике мы будем жарить сосиски на огне.

This sounds natural and straightforward:

• setting first: На пикнике
• subject: мы
• verb: будем жарить
• object: сосиски
• manner/location of cooking: на огне

Other orders are possible for emphasis, for example:

• Мы на пикнике будем жарить сосиски на огне.
• Сосиски мы будем жарить на огне.

These may shift focus, but the original sentence is a very natural default.

They both use на, but they express different kinds of meaning.

• на пикнике = at the picnic
  This gives the situation/event/location

• на огне = over the fire
  This gives the method/place of cooking

So they are both prepositional phrases, but they answer different questions:

• Где / когда? → на пикнике
• Где / как готовим? → на огне

Russian often uses the same preposition in several related ways, and the exact meaning depends on context.

The main stresses are:

• на пикни́ке
• мы бу́дем жа́рить соси́ски на огне́

Word by word:

• пикни́ке
• бу́дем
• жа́рить
• соси́ски
• огне́

This can help with pronunciation, especially because Russian stress is not always predictable.