Je vais au kiosque acheter le journal du matin.

Because aller is an irregular verb.

Its present-tense forms are:

• je vais = I go / I am going
• tu vas
• il / elle / on va
• nous allons
• vous allez
• ils / elles vont

So with je, the correct form is vais.

Because à + le contracts to au in French.

So:

• à le kiosque → au kiosque

This is a standard contraction:

• à + le = au
• à + les = aux

So je vais au kiosque means I’m going to the kiosk/newsstand.

In this sentence, un kiosque usually means a newsstand or newspaper kiosk, not just any kiosk.

So au kiosque suggests a place where newspapers and magazines are sold.

Depending on context, kiosque can also mean other kinds of small booths or stands, but here the presence of le journal makes newsstand the most natural interpretation.

Because it expresses the purpose of going there: you go somewhere to do something.

So:

• Je vais au kiosque acheter le journal
  = I’m going to the kiosk to buy the newspaper

After a verb of movement like aller, French often uses the infinitive directly to show purpose, especially in simple everyday sentences.

It works like:

• Je vais au marché acheter des fruits.
• Il est sorti chercher du pain.

French often leaves out pour after verbs of movement when the purpose is obvious.

So both of these are possible:

• Je vais au kiosque acheter le journal.
• Je vais au kiosque pour acheter le journal.

The version without pour is very natural and common. It sounds a bit more direct and streamlined.

Using pour is not wrong; it just makes the purpose more explicitly stated.

Not exactly.

French has a near-future structure:

• je vais acheter = I’m going to buy

But in your sentence, the structure is different:

• je vais au kiosque acheter...

Here, vais keeps its basic meaning of go:

• I’m going to the kiosk to buy...

So this is not mainly the future tense. It is a sentence about movement to a place, followed by the purpose of that movement.

Compare:

• Je vais acheter le journal. = I’m going to buy the newspaper.
• Je vais au kiosque acheter le journal. = I’m going to the kiosk to buy the newspaper.

Le is the definite article, so it means the newspaper.

French often uses the definite article in places where English might also use the, especially when the thing is specific, expected, or understood from context.

Here, le journal du matin suggests:

• the morning paper
• the newspaper someone normally buys in the morning
• the specific newspaper being referred to in the situation

If you said un journal du matin, it would sound more like a morning newspaper, one among others.

Du matin literally means of the morning, but in natural English it usually corresponds to morning in phrases like:

• le journal du matin = the morning newspaper / the morning paper

This is a very common French pattern:

• le café du matin = morning coffee
• les nouvelles du soir = the evening news

So du matin describes what kind of newspaper it is: the one for the morning.

Because du is the contraction of de + le.

So:

• de le matin → du matin

This contraction is required in normal French.

Here, de links the noun journal to matin:

• le journal du matin
• literally: the newspaper of the morning

Just like:

• la lumière du soleil = the light of the sun
• le début du film = the beginning of the film

Because the sentence first gives the destination, then the purpose.

So the structure is:

• Je vais = I’m going
• au kiosque = to the kiosk
• acheter le journal du matin = to buy the morning newspaper

This order is very natural in French:

1. movement
2. place
3. purpose

It helps the sentence flow clearly:

• where are you going?
• why are you going there?

Yes, that is possible, but it shifts the focus a little.

• Je vais au kiosque acheter le journal
  Focuses first on going to the kiosk

• Je vais acheter le journal au kiosque
  Focuses more on buying the newspaper, with au kiosque as the place where that happens

Both are grammatical. The original version feels especially natural if the important idea is the trip to the kiosk.

Not always.

Un journal can mean:

• a newspaper
• a journal/diary, in some contexts

But in everyday French, when you say acheter le journal, it usually means buy the newspaper.

If you mean a personal diary, the context usually makes that clear, or French may use expressions like:

• un journal intime = a diary

So in this sentence, journal definitely means newspaper.