Learn Hardcore French: Dans notre quartier, les habitants essaient de produire moins de déchets. - In our neighborhood, the residents try to produce less waste.

In French, dans is used for something happening inside a physical space or area, like a neighborhood, room, or city: dans le quartier, dans la ville, dans la maison.
À is used more with points or places you go to or are at: à l’école, à Paris, à la plage.
Here we mean “within the area of our neighborhood,” so dans notre quartier is the natural choice. À notre quartier would sound wrong to a native speaker.

Could we also say Les habitants de notre quartier essaient… instead of starting with Dans notre quartier?

Yes. Two natural possibilities are:

Dans notre quartier, les habitants essaient de produire moins de déchets.
Les habitants de notre quartier essaient de produire moins de déchets.

Both are correct and mean almost the same thing.
The first starts by setting the place as the topic (“As for our neighborhood…”).
The second starts with the people and specifies which ones using de notre quartier (“The inhabitants of our neighborhood…”).

What exactly does les habitants mean? Is it different from les gens or les résidents?

Les habitants literally means “the inhabitants,” that is, the people who live in a particular place.
Compared to similar words:

les habitants = the people who live in a place (quite general, common in everyday speech and writing)
les gens = “people” in a very general sense, not tied to a specific place
les résidents = “residents”; sounds a bit more formal or administrative (e.g. residents of a nursing home, residents of a building)

So les habitants is a natural, neutral way to say “the people who live there.”

Why is it essaient de produire and not essaient produire or essaient à produire?

After the verb essayer, when it is followed by another verb, French normally uses de + infinitive:

essayer de faire = to try to do
essayer de comprendre = to try to understand
essayer de produire = to try to produce

Using essayer produire (without de) or essayer à produire would be incorrect here. The pattern you should remember is essayer de + infinitive.

I’ve seen both ils essaient and ils essayent. Which is correct?

Both ils essaient and ils essayent are officially correct spellings of the 3rd person plural of essayer in the present tense.

ils essaient (with i) is more common in modern written French.
ils essayent (with y) is also accepted and used, especially in speech or less formal writing.

They are pronounced the same in everyday speech: roughly [ilé-sè-ye]. In your sentence, les habitants essaient is perfectly standard.

Does essaient mean “try” or “are trying”? Why is there no separate continuous tense?

French doesn’t have a separate continuous tense like English “are trying”.
The simple present ils essaient can translate as both:

They try
They are trying

Context tells you which is more natural in English. Here, “the inhabitants are trying to produce less waste” is the best translation, but the French form is just the simple present.

Why use produire instead of faire for “produce”?

Both produire and faire can sometimes be translated as “to produce,” but:

produire is the standard verb for “to produce” in a more concrete or technical sense: produire de l’électricité, produire des biens, produire des déchets.
faire is more general (“to do/make”) and would sound less natural in this context.

So produire moins de déchets is the idiomatic way to say “produce less waste” or “generate less waste.”

Why is it moins de déchets and not moins des déchets?

With expressions of quantity, French normally uses de without an article:

beaucoup de déchets (a lot of waste)
peu de déchets (little/few waste)
trop de déchets (too much waste)
moins de déchets (less waste)

So after moins, you must say moins de + noun.
Moins des déchets would be wrong here; it would suggest “less of the specific waste,” which is not the general idea in this sentence.

Why is déchets plural, when English often says “waste” in the singular?

In French, un déchet is one piece/item of waste, and des déchets is “waste” in general.
Even when English uses the uncountable singular waste, French normally uses the plural déchets:

réduire ses déchets = to reduce one’s waste
les déchets ménagers = household waste

So moins de déchets is the natural French expression, even though in English we say “less waste.”

Are there other common words for “waste” besides déchets?

Yes, a few frequent ones:

les déchets – general word for waste/garbage (very common)
les ordures – rubbish/garbage (often what you put in the bin)
les poubelles – literally “trash cans,” but often used to mean “garbage” in everyday speech: sortir les poubelles = take out the trash

In your sentence, déchets is exactly the right register: neutral and widely used in environmental contexts.

Is there any important pronunciation to know in les habitants essaient de produire moins de déchets?

Yes, a few points:

les habitants: there is a liaison, so it’s pronounced roughly [lé-zabitan], not [lé abitan].
Final consonants s, t are silent at the ends of les, habitants, moins, déchets in normal speech.
essaient is pronounced the same as essai plus a nasal -ent ending: roughly [é-sè]; the written -ent is silent.

So the whole main clause flows together something like: [lé-zabitan é-sè de prodɥiR mwɛ̃ də déʃɛ].