Этот квартал был трудным.

Because трудным is in the instrumental case, masculine singular.

In this sentence, трудным is a predicate adjective after был. In Russian, after forms of быть in the past or future, an adjective describing what something was / will be is very often put in the instrumental:

• Он был счастливым.
• День был долгим.
• Этот квартал был трудным.

So the dictionary form is трудный, but here it changes to трудным.

Yes, you may encounter that, but Этот квартал был трудным is the more standard and expected choice.

With predicate adjectives after быть, Russian can use:

• instrumental: был трудным
• sometimes nominative: был трудный

The instrumental is especially common when describing a state, quality, or role in the past. For a learner, it is safest to use:

• был трудным
• была трудной
• было трудным
• были трудными

So while был трудный is not impossible, был трудным is the version you should learn first.

Because квартал is a masculine singular noun.

In the past tense, Russian verbs agree with the subject in gender and number:

• masculine singular: был
• feminine singular: была
• neuter singular: было
• plural: были

Since этот квартал is masculine singular, the verb must be был.

A good clue is its ending: квартал ends in a consonant, and nouns like that are often masculine in Russian.

You can also see it from the words agreeing with it:

• этот = masculine singular
• был = masculine singular

So the sentence itself shows you that квартал is being treated as masculine.

It is in the nominative case, because it is the subject of the sentence.

The subject is the thing being talked about: this quarter.

Both words are nominative masculine singular:

• этот = nominative masculine singular of this
• квартал = nominative singular

Квартал can mean different things depending on context, most commonly:

• a quarter of a year, especially in business or reporting
• a city block
• sometimes an urban district / neighborhood area

In a sentence like Этот квартал был трудным, the most likely meaning is this quarter in the time/business sense, especially if the meaning has already been provided to the learner.

So this is one of those nouns where context matters a lot.

Этот means this and must agree with the noun it modifies.

Because квартал is masculine singular nominative, the demonstrative also takes the masculine singular nominative form:

• masculine: этот
• feminine: эта
• neuter: это
• plural: эти

So:

• этот квартал
• эта неделя
• это время
• эти дни

Yes. Russian word order is more flexible than English, although not completely free.

The neutral order here is:

• Этот квартал был трудным.

But you could also see:

• Трудным был этот квартал.
• Был трудным этот квартал.

These alternatives change the emphasis or sound more literary or marked. For everyday neutral usage, Этот квартал был трудным is the best choice.

In the present tense, yes. In the past tense, no.

Russian often omits to be in the present:

• Этот квартал трудный. = This quarter is difficult.

But in the past tense you need the past form of быть:

• Этот квартал был трудным. = This quarter was difficult.

So the verb is omitted in the present, but expressed in the past and future.

Because трудный normally appears here as a long-form adjective.

Russian has both long and short adjective forms, but not every adjective uses the short form equally often in modern speech. The long form after быть is very common and natural:

• Он был счастливым.
• Путь был долгим.
• Этот квартал был трудным.

A short form of трудный does exist in some contexts, but for this sentence, был трудным is the natural standard pattern for learners to use.

Almost, but not exactly the same in structure.

• Этот квартал был трудным. = This quarter was difficult.
• Это был трудный квартал. = It was a difficult quarter.

The second sentence uses это as it/this, and then identifies what it was: a difficult quarter.

Also notice that in Это был трудный квартал, the adjective is often left in the nominative because it is part of the noun phrase трудный квартал, not standing alone as a predicate adjective.

They are similar, but not always identical.

• трудный often means difficult / hard
• сложный often means complex / complicated, though it can also mean difficult

So:

• трудный квартал suggests a quarter that was hard, challenging, demanding
• сложный квартал could suggest a quarter that was complicated, difficult, or problematic in a more complex way

In many contexts both could work, but трудный is a very natural choice for a difficult quarter.

You would change all the agreeing words:

• Эти кварталы были трудными.

Changes:

• этот → эти
• квартал → кварталы
• был → были
• трудным → трудными

This is a good example of how Russian agreement works across the whole sentence.