Learn Hardcore Greek: Η ζωή στην πόλη είναι δύσκολη.

Η ζωή literally is the life, but in many contexts it translates as just life.
In general, Greek tends to use the article with abstract nouns (like ζωή = life, αγάπη = love, ελευθερία = freedom) where English often omits it.

So Η ζωή στην πόλη είναι δύσκολη is naturally translated as Life in the city is difficult, not The life in the city is difficult, even though the Greek has the article.

What does στην mean exactly, and why is it written as one word?

Στην is a combination of two words:

σε = in / at / to
την = the (feminine singular accusative)

So:

σε + την πόλη → στην πόλη

In speech these merge, and in modern Greek spelling they are normally written as one word: στον, στην, στο, στη, etc., depending on the gender and number of the noun that follows.

What case is πόλη in here, and why?

Πόλη is in the accusative case here.

Reason:

The preposition σε (in, at, to) is followed by the accusative.
So σε + την πόλη puts πόλη in the accusative: την πόλη.

For this noun, η πόλη (the city), the nominative and accusative singular forms are the same in writing:

Nominative: η πόλη (subject)
Accusative: την πόλη (object / after a preposition)

So πόλη looks the same, but grammatically it is accusative in this sentence.

Where is the article the for πόλη? I only see στην πόλη, not την πόλη.

The article την is actually inside the form στην.

Recall:

στην = σε
- την

So:

στην πόλη really is σε την πόλη, literally in the city.

You do not write σε την πόλη separately in modern Greek; you use the merged form στην πόλη.

Why is it είναι δύσκολη and not something like είναι δύσκολο?

In Greek, adjectives must agree with the noun they describe in:

gender (masculine / feminine / neuter)
number (singular / plural)
case (nominative / accusative / etc.)

Here:

ζωή (life) is feminine, singular, nominative (it is the subject).
Therefore, the adjective δύσκολος (difficult) must also be feminine singular nominative: δύσκολη.

So:

η ζωή είναι δύσκολη = life is difficult.
το πράγμα είναι δύσκολο (neuter) = the thing is difficult.
ο καιρός είναι δύσκολος (masculine) = the weather is difficult / hard.

Why is there no word for it in είναι δύσκολη? In English we say it is difficult.

Greek often omits subject pronouns when they are clear from context or from the verb form.

The subject here is η ζωή στην πόλη (life in the city).
So you do not need a separate it.

English structure:

Life in the city is difficult.
(You might also say It is difficult to live in the city, where it is a dummy subject.)

Greek structure:

Η ζωή στην πόλη είναι δύσκολη.
There is no dummy it in Greek; the subject is the noun itself (η ζωή).

Can I change the word order to Η ζωή είναι δύσκολη στην πόλη? Does it sound natural?

Yes, that is grammatically correct and natural.

Η ζωή στην πόλη είναι δύσκολη.
- Slight emphasis on in the city as part of the subject: Life in the city (as opposed to life elsewhere) is difficult.
Η ζωή είναι δύσκολη στην πόλη.
- Slight emphasis on where life is difficult: life is difficult in the city (implying maybe it is easier elsewhere).

Both are fine; Greek word order is flexible, and subtle differences in emphasis arise from different placements, but both versions are natural.

How do you pronounce the whole sentence?

In a simple phonetic transcription (approximate IPA):

Η → [i]
ζωή → [zoˈi]
στην → [stin]
πόλη → [ˈpoli]
είναι → [ˈine]
δύσκολη → [ˈðiskoli]

Together:

Η ζωή στην πόλη είναι δύσκολη. → [i zoˈi sti ˈpoli ˈine ˈðiskoli]

Main stress on the syllables marked with ´: ζωή, πόλη, είναι, δύσκολη.

Why does ζωή have an accent on the last letter ή?

In Greek, every word of two or more syllables must have one main stress marked with an accent (´) on a vowel.

ζωή has two syllables: ζω–ή.
The stress is on the second syllable, so the accent is placed on ή: ζωή.

The accent mark tells you both:

Where to place the stress when pronouncing.
Which syllable changes (or not) when the word is inflected (conjugated/declined).

So ζωή is pronounced zo-Í, not ZÓ-i.

What gender is ζωή, and how can I tell?

Ζωή is a feminine noun.

Clues:

It takes the feminine article η: η ζωή.
Many feminine nouns end in -η in the nominative singular.

Typical pattern:

η ζωή (nominative) – life
τη ζωή (accusative) – the life (object)
της ζωής (genitive) – of the life

You generally have to learn the gender with the noun, but endings like -η, -α, -ος (in many cases) are common for feminine nouns.

What gender is πόλη, and what is its basic form in the dictionary?

Πόλη is also feminine.

The dictionary (nominative singular) form is η πόλη = the city.

Basic singular forms:

Nominative: η πόλη (subject)
Accusative: την πόλη (object / after prepositions)
Genitive: της πόλης (of the city)

Again, the article η tells you it is feminine, and the ending -η is typical for many feminine nouns.

Why does δύσκολη end in -η and not -ος like the base adjective δύσκολος?

The base dictionary form of the adjective is δύσκολος (masculine nominative singular).

Greek adjectives have different endings depending on gender and case:

Masculine: δύσκολος (for ο nouns, e.g. ο καιρός είναι δύσκολος)
Feminine: δύσκολη (for η nouns, e.g. η ζωή είναι δύσκολη)
Neuter: δύσκολο (for το nouns, e.g. το πρόβλημα είναι δύσκολο)

In this sentence:

The noun ζωή is feminine.
Therefore, the adjective must be in the feminine form: δύσκολη.

Is στην πόλη always in the city, or can it also mean to the city?

Σε is a very flexible preposition in Greek and can mean in, at, or to, depending on context:

στην πόλη can mean:
- in the city (location)
- to the city (movement / direction), depending on the verb.

Examples:

Μένω στην πόλη. → I live in the city.
Πηγαίνω στην πόλη. → I am going to the city.

In your sentence, Η ζωή στην πόλη είναι δύσκολη, the context is clearly location, so the correct translation is in the city.