Learn Hardcore French: Mes parents ont promis qu'ils nous aideraient si nous avions des problèmes de logement. - My parents promised that they would help us if we had housing problems.

Ont promis is the passé composé of promettre and it presents the promise as a completed event at a specific point in the past (they promised, once).

Mes parents ont promis… → “My parents promised / have promised…” (a single act).
Mes parents promettaient… would be imparfait, suggesting a repeated habit or an ongoing background action (“they used to promise / they were promising”).
Mes parents promirent… is the passé simple, used mainly in formal/literary written French, not in everyday speech.

So ont promis is the normal spoken and written form to describe a concrete promise made in the past.

Why is it qu'ils nous aideraient and not qu'ils nous aideront?

Aideraient is the conditional (conditionnel présent). In this sentence it has two roles:

Future in the past / reported speech:
- Direct speech (original promise):
  « Nous vous aiderons si vous avez des problèmes de logement. »
- Reported later:
  Mes parents ont promis qu'ils nous aideraient si nous avions des problèmes de logement.
  French usually “backshifts” future → conditional when reporting a past statement.
It also matches the si + imparfait → conditionnel structure:
- si nous avions…, ils nous aideraient…

You can sometimes hear ont promis qu'ils nous aideront if the speaker wants to stress that the help is still very clearly in the future and felt as certain, but the conditional is the standard form in careful French for this type of reported promise.

In the si clause, why is it si nous avions des problèmes (imparfait) and not si nous avons des problèmes?

French has several standard if-clause patterns. For hypothetical or less certain situations, the normal pattern is:

si + imparfait → conditionnel présent
- Si nous avions des problèmes, ils nous aideraient.
  (“If we had problems, they would help us.”)

Using si nous avons des problèmes would sound more like a neutral, real possibility in the future and normally calls for the future in the main clause:

Si nous avons des problèmes, ils nous aideront.
(“If we have problems, they will help us.”)

In your sentence, the structure is hypothetical and reported, so si nous avions … aideraient is the expected combination.

Why is si nous aurions des problèmes wrong?

In standard French, when si means “if” (introducing a condition), it is never followed by the future or the conditional.

The correct patterns are:

si + présent → futur / impératif / présent
si + imparfait → conditionnel présent
si + plus-que-parfait → conditionnel passé

So you must say:

Si nous avions des problèmes, ils nous aideraient.
and not Si nous aurions des problèmes, ils nous aideraient.

Could we also say Mes parents ont promis de nous aider si nous avions des problèmes de logement? Is it different from ont promis qu'ils nous aideraient?

Yes, Mes parents ont promis de nous aider… is correct and natural.

Promettre de + infinitif:
Mes parents ont promis de nous aider…
Focuses on the action itself (they promised to help us).
Promettre que + proposition:
Mes parents ont promis qu'ils nous aideraient…
Focuses on the content of what they said, in full-sentence form.

The meaning is essentially the same in this context. The que + clause version allows you to play more with tenses (future in the past, etc.), but both are fine.

Why is the word order ils nous aideraient and not ils aideraient nous, like in English “they would help us”?

In French, object pronouns like me, te, nous, vous, le, la, lui, leur, y, en usually go before the conjugated verb:

Ils nous aideraient. → “They would help us.”
Il me parle. → “He talks to me.”

So ils aideraient nous is incorrect.

With an infinitive, the pronoun goes before the infinitive:

Ils vont nous aider. (“They are going to help us.”)
Ils ont promis de nous aider. (“They promised to help us.”)

Why des problèmes and not de problèmes or les problèmes?

Here des problèmes is a plural indefinite article (“some problems” / “any problems”). The idea is not specific problems that we already know about, but problems in general:

avoir des problèmes → “to have problems / to have trouble”

Comparisons:

Ils n’ont pas de problèmes. (negative → de, not des)
Ils ont beaucoup de problèmes. (after a quantity → de problèmes)
les problèmes de logement would refer to “the housing problems” in a specific, already identified context.

So des problèmes is normal because it’s a positive statement with an unspecified number of possible problems.

Why do we say des problèmes de logement and not something like des problèmes avec le logement or des problèmes du logement?

French often uses nom + de + nom to show the type of problem:

un problème de santé → a health problem
un problème d’argent → a money problem
des problèmes de logement → housing problems

Problèmes avec le logement is possible, but it sounds more like a conflict with or an issue with a particular thing, and it’s less idiomatic here.

Problèmes du logement would normally sound like “the problems of the housing” and is not the usual way to say “housing problems” in general.

So des problèmes de logement is the natural fixed expression for “housing problems / problems with accommodation.”

What exactly does logement mean, and how is it different from maison or appartement?

Logement is a general, fairly formal word meaning “accommodation / housing / a place to live.” It does not specify the type.

un logement → a dwelling, a place to live (could be a flat, a house, a studio, etc.)
une maison → a house
un appartement → an apartment / flat

So des problèmes de logement means “housing problems / accommodation problems” in general, not specifically “problems with our house” or “with our apartment.”

Why is it written qu'ils with an apostrophe and not que ils?

This is elision. In French, some small words ending in -e drop that vowel before a word starting with a vowel sound, and they are written with an apostrophe:

que + ils → qu'ils
je + ai → j’ai
ne + avons → n’avons

So que ils becomes qu’ils, pronounced in one smooth unit. Writing que ils would be incorrect in standard French.

Why do we use ils after que, and not eux?

In this sentence, ils is the subject pronoun of the verb aideraient:

qu’ (conjunction that) + ils (subject) + nous aideraient (verb + object).

Eux is a stressed (disjunctive) pronoun, used in positions like:

After a preposition: avec eux, pour eux
For emphasis: Eux, ils nous aideraient.

Since we need a grammatical subject here, ils is required:
qu’ils nous aideraient, not que eux nous aideraient.

In Mes parents ont promis, why is it ont and not a? And why doesn’t promis change form?

Mes parents is third person plural, so the auxiliary avoir must also be plural:

ils ont, mes parents ont, mes amis ont
vs.
il a, mon père a

So you say Mes parents ont promis, not a promis.

The past participle promis doesn’t change because:

With avoir as auxiliary, the participle usually does not agree with the subject.
It would only agree with a direct object placed before the verb, which we don’t have here.

So promis stays the same for all subjects: il a promis, ils ont promis, elles ont promis, etc.

Could we also say Mes parents ont promis qu’ils nous aideront si nous avons des problèmes de logement? Would that be wrong?

It’s not wrong, and you will hear/read it. The nuance is:

ont promis qu’ils nous aideraient si nous avions…
→ more consistent reported speech / future-in-the-past, slightly more formal and “textbook-correct.”
ont promis qu’ils nous aideront si nous avons…
→ the speaker keeps the statement close to present reality, as if the parents are still making a living, current promise about the future.

Both are grammatically accepted. For strict indirect speech from a past point of view, French grammars prefer aideraient / avions, but in everyday speech people often keep aideront / avons when the promise is still clearly about the future and felt as very certain.