Этот сборник рассказов оказался интереснее, чем я ожидал.

Because этот сборник is the subject of the sentence, so it is in the nominative case.

• этот = this (masculine nominative singular)
• сборник = collection / anthology (masculine nominative singular)

The main thing being talked about is the collection, so Russian uses the nominative here.

This is a very common Russian pattern:

• сборник рассказов = a collection of stories
• рассказов is genitive plural of рассказ

After nouns like сборник (collection), группа (group), куча (pile), пачка (pack), Russian often puts the second noun in the genitive to show what the collection consists of.

So:

• сборник стихов = a collection of poems
• сборник статей = a collection of articles
• сборник рассказов = a collection of stories

Оказаться means something like:

• to turn out to be
• to prove to be

So оказался интереснее means not just was more interesting, but turned out to be more interesting than expected.

That gives the sentence a sense of result or discovery.

Compare:

• Сборник был интересный = The collection was interesting.
• Сборник оказался интересным = The collection turned out to be interesting.
• Сборник оказался интереснее, чем я ожидал = The collection turned out to be more interesting than I expected.

Because the subject is сборник, which is:

• masculine
• singular

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

So:

• сборник оказался — masculine singular
• книга оказалась — feminine singular
• письмо оказалось — neuter singular
• книги оказались — plural

Even though рассказов is plural, it is not the main subject. The head noun is сборник, so the verb agrees with сборник.

Интереснее is the comparative form of интересный and means more interesting.

Here the sentence is making a comparison:

• интереснее, чем... = more interesting than...

So the comparative is required.

Why not the other forms?

• интересным = interesting in the instrumental case, not comparative
• более интересный is also possible in some contexts, but интереснее is the more natural simple comparative here

So:

• оказался интересным = turned out to be interesting
• оказался интереснее = turned out to be more interesting

Russian comparative forms like интереснее are usually indeclinable in this kind of use. That means they do not change for:

• gender
• number
• case

So the same form can be used with different subjects:

• фильм интереснее
• книга интереснее
• рассказы интереснее

This is normal for the simple comparative.

Чем is the usual word for than in comparisons.

So:

• интереснее, чем я ожидал = more interesting than I expected

This is one of the most common comparison patterns in Russian:

• лучше, чем... = better than...
• хуже, чем... = worse than...
• больше, чем... = more than...
• интереснее, чем... = more interesting than...

The object is omitted because it is understood from context.

Literally, the idea is:

• more interesting than I expected [it to be]

Russian often leaves out words that are obvious. Here, the listener already knows we are talking about the collection.

So чем я ожидал naturally means:

• than I expected
• more fully: than I expected it would be

This kind of omission is very common and sounds natural.

Because Russian does not need to repeat the object when it is already clear.

If you added an object, it would usually sound unnecessary here. The comparison already tells us what is being compared.

So:

• чем я ожидал = than I expected

is the most natural version.

The past tense in Russian also shows the speaker’s gender when the subject is я.

So:

• я ожидал = I expected if the speaker is male
• я ожидала = I expected if the speaker is female

The sentence you have uses a male speaker. A female speaker would say:

• Этот сборник рассказов оказался интереснее, чем я ожидала.

Yes. Russian word order is flexible, although the original version is the most neutral and natural:

• Этот сборник рассказов оказался интереснее, чем я ожидал.

You might also hear:

• Сборник рассказов оказался интереснее, чем я ожидал.
• Интереснее, чем я ожидал, оказался этот сборник рассказов.

But changing the order usually changes the focus or emphasis. For a normal statement, the original order is best.

Yes. Оказаться is perfective.

That matters because the sentence describes a completed realization: after reading or looking at the book, the speaker came to the conclusion that it was more interesting than expected.

The imperfective partner is оказываться, which would be used in different contexts, for example for repeated situations or general statements.

Here, perfective оказался fits because it expresses a single outcome:

• it turned out to be more interesting

Yes, but the meaning would change.

• Этот сборник рассказов был интереснее, чем я ожидал. = This collection of stories was more interesting than I expected.

• Этот сборник рассказов оказался интереснее, чем я ожидал. = This collection of stories turned out to be more interesting than I expected.

The version with оказался sounds more natural when the speaker wants to stress that the result was somewhat surprising or different from expectation.