Turneden önce figüranla birlikte oyunu sahneleyeceğiz.

Because önce normally takes the ablative case when it follows a noun.

• turne = tour
• turneden önce = before the tour

So the pattern is:

• X-den / -dan önce = before X

Examples:

• dersten önce = before class
• yemekten önce = before the meal

If you want to say before doing something, Turkish usually uses a different structure:

• gitmeden önce = before going
• başlamadan önce = before starting

More or less, yes.

• figüranla = with the extra / with the supporting performer
  
  • This -la is the attached form of ile = with
• birlikte = together

So figüranla birlikte means together with the extra.

This is very natural in Turkish and not strange. It adds a little emphasis to the idea of doing something jointly.

You could also say:

• figüranla sahneleyeceğiz
• figüran ile birlikte sahneleyeceğiz

They are all possible, but -la birlikte sounds nicely explicit.

Because of vowel harmony.

The suffix is -la / -le, and the form depends on the last vowel of the word.

• figüran ends in the vowel a
• a is a back vowel
• so the suffix becomes -la

So:

• figüranla = with the extra

Compare:

• öğretmenle = with the teacher
• arkadaşla = with the friend

Because of the context.

oyun can mean both:

• game
• play (theatrical play)

In this sentence, several words point to the theater meaning:

• figüran = extra / supporting performer
• turne = tour
• sahnelemek = to stage / put on

So here oyun clearly means a play, not a game.

Because it is the direct object of the verb, and it is a specific/definite one.

• oyun = a play / play in general
• oyunu = the play / a specific play

Turkish often marks a specific direct object with the accusative ending.

Here:

• oyun + u → oyunu

So oyunu sahneleyeceğiz means we will stage the play.

If the meaning were more like we will stage a play, Turkish would more naturally say:

• bir oyun sahneleyeceğiz

It is made from:

• sahnele- = to stage
• -(y)ecek / -(y)acak = future tense
• -iz / -ız / -uz / -üz = we

So the structure is:

• sahnele- + y + ecek + iz

which becomes:

• sahneleyeceğiz = we will stage

So the whole verb means we will stage.

That y is a buffer consonant.

The verb stem sahnele- ends in a vowel, and the future suffix also begins with a vowel. Turkish usually inserts y between vowels to make pronunciation smoother.

So instead of something awkward like:

• sahneleecek...

Turkish uses:

• sahneleyecek...

The same thing happens in many words:

• başla-y-acak
• bekle-y-ecek
• anla-y-acağız

It can often match either will or be going to in English, depending on context.

Here it simply gives a normal future meaning:

• sahneleyeceğiz = we will stage / we are going to stage

In many cases, Turkish does not sharply separate those two English ideas. The form just says that the action is in the future, often with a sense of plan or intention.

Because Turkish is usually a verb-final language.

A very common basic order is:

• time
• other information
• object
• verb

So in this sentence:

• Turneden önce = before the tour
• figüranla birlikte = together with the extra
• oyunu = the play
• sahneleyeceğiz = we will stage

This is normal Turkish word order, even though English would arrange the sentence differently.

Yes. Turkish word order is fairly flexible, as long as the endings make the roles clear.

For example, these are also possible:

• Turneden önce oyunu figüranla birlikte sahneleyeceğiz.
• Oyunu turneden önce figüranla birlikte sahneleyeceğiz.

The core meaning stays basically the same, but the focus shifts a little depending on what the speaker wants to emphasize.

Still, keeping the verb at the end is the most typical pattern.