Marie acceptera de cuisiner pour nous à condition que personne ne se plaigne et que tout le monde l’aide.

Acceptera is the simple future of accepter.

The sentence is talking about what Marie will agree to do, not what she agrees to do right now. In English, we might say Marie will agree to cook for us..., and French uses the future tense in the same kind of way here.

• elle accepte = she agrees / she is agreeing
• elle acceptera = she will agree

So Marie acceptera de cuisiner... means that her agreement depends on the conditions that follow.

After accepter, French normally uses de before another infinitive.

So:

• accepter de faire quelque chose = to agree to do something

Examples:

• J’accepte de venir. = I agree to come.
• Elle accepte de cuisiner. = She agrees to cook.

This is just the standard pattern of the verb. English often goes straight from agree to to + verb, but French needs de here.

À condition que means provided that, as long as, or on condition that.

It introduces a condition:

• Marie acceptera de cuisiner... à condition que...
• Marie will agree to cook... provided that...

The que is part of the fixed expression à condition que. After it, French introduces a full clause with its own verb.

So:

• à condition de + infinitive is possible in some cases
• but here we have à condition que + verb

Because the sentence gives specific conditions involving other people, the full clause is needed:

• à condition que personne ne se plaigne
• à condition que tout le monde l’aide

They are in the subjunctive because à condition que requires the subjunctive.

This is very common in French: certain conjunctions trigger the subjunctive because they express things like condition, doubt, emotion, purpose, or uncertainty.

Here:

• se plaigne is the subjunctive of se plaindre
• aide is the subjunctive of aider

So:

• à condition que personne ne se plaigne
• et que tout le monde l’aide

Both are part of the condition, so both verbs stay in the subjunctive.

Because personne already carries the negative meaning of nobody / no one.

In French, personne used as no one is normally paired with ne, but not with pas.

So:

• Personne ne vient. = Nobody is coming.
• Personne ne se plaint. = Nobody is complaining.

In your sentence:

• personne ne se plaigne = that nobody complain

If you added pas, it would be wrong in standard French here.

The verb is se plaindre, which means to complain.

It is a pronominal verb, so it includes se in its basic form:

• se plaindre = to complain

That means when you conjugate it, you keep the reflexive pronoun:

• je me plains
• tu te plains
• il/elle se plaint
• que personne ne se plaigne

Even though English just says complain, French uses the full verb se plaindre.

Because French normally repeats que when two coordinated clauses depend on the same expression.

Here the structure is:

• à condition que
  • clause 1
• et que
  • clause 2

So:

• à condition que personne ne se plaigne et que tout le monde l’aide

This is more natural and clearer than trying to use only one que for both clauses.

English can often avoid repeating that, but French very often keeps it.

Because both expressions are grammatically singular in French.

• personne = no one / nobody
• tout le monde = everyone

Even though they refer to multiple people in meaning, French treats them as singular for agreement.

So:

• personne ne se plaigne — singular subjunctive
• tout le monde l’aide — singular subjunctive

This is similar to English in some cases:

• Everyone is here, not Everyone are here.

L’ stands for la, and it refers to Marie.

So:

• tout le monde l’aide = everyone helps her

Because Marie is feminine singular, the object pronoun is la. Before a vowel sound, la becomes l’:

• la aide → l’aide

So the full idea is:

• que tout le monde l’aide
• that everyone help her

Here it is a verb, not the noun.

It comes from aider:

• qu’il aide
• qu’elle aide
• que tout le monde l’aide

The accent in aide does not automatically make it a noun. You have to look at the grammar of the sentence.

Here, after que, we need a verb for the clause:

• que tout le monde l’aide = that everyone help her

So this is the subjunctive form of aider.

Yes, se plaindre is somewhat irregular.

Its subjunctive forms are based on the stem plaign-:

• que je me plaigne
• que tu te plaignes
• qu’il/elle se plaigne
• qu’ils/elles se plaignent

So personne ne se plaigne uses the il/elle/on-type subjunctive form, because personne is singular.

This is one of those verbs whose spelling changes in certain forms, so it is worth memorizing as a pattern:

• infinitive: se plaindre
• present indicative: il se plaint
• present subjunctive: qu’il se plaigne

Not with exactly the same meaning.

• à condition que = provided that / on condition that
• pour que = so that / in order that

Your sentence is about a requirement or condition:

• Marie will agree, provided that nobody complains and everyone helps her.

If you used pour que, it would sound more like for the purpose that or so that, which changes the meaning.

So à condition que is the right choice here because the sentence is setting terms.