Pendant la fête, Marie distribue du gâteau à ses amis.

All three can relate to time, but they don’t behave exactly the same:

• pendant la fête = during the party, focusing on the time span.
• durant la fête = very close to pendant, but a bit more formal or literary; in everyday speech, pendant is more common.
• lors de la fête = at the time of the party / on the occasion of the party; it sounds slightly more formal and often introduces a specific event that takes place then.

In normal conversational French, pendant la fête is the most neutral and common way to say during the party.

• la fête = the party, a specific party that the speaker and listener both know about (for example, the party they’ve been talking about).
• une fête = a party, any party, not previously identified.

Using la fête implies the party is already identified in the context, like during the (aforementioned/known) party.

In isolation, the present distribue means is distributing / distributes now.

If this sentence came from a story, French sometimes uses the présent de narration (narrative present) to make the action feel vivid, even when talking about the past; English often uses the past in such cases.

Grammatically:

• Marie distribue du gâteau = Marie distributes / is distributing cake.
• Marie a distribué du gâteau = Marie distributed / has distributed cake (completed in the past).

So distribue is simple present. To talk clearly about a past event, you’d normally use a distribué.

The infinitive is distribuer (to distribute, to hand out).

It’s a regular -er verb. Present tense (indicative):

• je distribue
• tu distribues
• il / elle / on distribue
• nous distribuons
• vous distribuez
• ils / elles distribuent

In the sentence, Marie distribue uses the il/elle form.

du gâteau uses the partitive article:

• du gâteau = some cake / cake (an unspecified amount). It’s treating cake as a mass/uncountable quantity.
• le gâteau = the cake (a specific cake as a whole).
• un gâteau = a cake (one entire cake, countable item).
• des gâteaux = cakes (more than one cake).

Here, Marie is giving her friends some cake, not necessarily a whole cake each, so French uses the partitive du gâteau.

Yes.

• gâteau is masculine singular.
• The partitive with a masculine singular noun is du, which is the contraction of de + le.

So literally du gâteau = some of the cake / some cake. The contraction du is mandatory: you cannot say de le gâteau.

In French, the indirect object of distribuer (who receives what is being distributed) is introduced with à:

• distribuer quelque chose à quelqu’un = to distribute something to someone.

So:

• distribue du gâteau à ses amis = distributes cake to her friends.

pour would mean for, and suggests purpose or benefit, not direct receiving.
For example:

• Elle prépare un gâteau pour ses amis. = She prepares a cake for her friends (for their benefit, not necessarily handing it directly to them yet).

Yes, you can say:

• Marie distribue du gâteau à ses amis.
• Marie distribue à ses amis du gâteau.

Both are grammatically correct and mean the same thing.

French tends to put the direct object (here: du gâteau) before the indirect object (here: à ses amis), especially when both are noun phrases. The first version sounds slightly more natural and common in everyday speech.

• pendant la fête = during the party, focusing on the time period.
• à la fête = at the party, focusing on the place/event as a location.

You could say:

• À la fête, Marie distribue du gâteau à ses amis.
  → At the party, Marie hands out cake to her friends.

That’s also correct, but it slightly shifts the emphasis from the time span (during) to the location/event (at).

Yes, a couple of points:

• Pendant la fête:

  • Final t in fête is silent.
  • No liaison between pendant and la in standard speech.

• du gâteau:

  • Final u in du sounds like French u [y], not like English doo.
  • gâteau ≈ ga-toh; final -eau is [o].

• ses amis:

  • There is a liaison: ses‿amis. You pronounce the s in ses like a z linked to amis: sé-zami.