Этот сырок лежал в холодильнике до вечера, и брат съел его после работы.

Because этот has to agree with сырок in gender, number, and case.

• сырок is masculine singular
• the noun is in the nominative case here

So the correct form is этот.

Compare:

• этот сырок = this cheese snack/bar
• эта книга = this book
• это окно = this window
• эти продукты = these groceries

Сырок is a diminutive form related to сыр (cheese), but in real usage it often means a small cheese item or a curd snack/bar, depending on context.

So in this sentence it is not necessarily “a tiny piece of regular cheese.” It could mean:

• a little cheese snack
• a curd bar
• a small cheese item

The exact English translation depends on context and region.

Russian often uses specific verbs for the position of objects:

• лежать = to lie
• стоять = to stand
• висеть = to hang

So сырок лежал в холодильнике literally means the cheese snack was lying in the fridge.

This is very natural in Russian. English often just says was in the fridge, but Russian frequently prefers a positional verb.

If you said был в холодильнике, that would also be understandable, but it is less vivid and less specific. лежал tells you how the object was situated.

Because the sentence is talking about the past.

• лежит = is lying / lies
• лежал = was lying / lay

So:

• Этот сырок лежит в холодильнике = This cheese snack is in the fridge.
• Этот сырок лежал в холодильнике = This cheese snack was in the fridge / was lying in the fridge.

That is the normal marker of the past tense in Russian. In the past tense, verbs also agree with the subject in gender and number.

Here:

• лежал = masculine singular past
• лежала = feminine singular past
• лежало = neuter singular past
• лежали = plural past

Since сырок is masculine singular, you get лежал.

The same thing happens with съел: it is also masculine singular past, because брат is masculine singular.

Because в холодильнике answers the question where?

• в холодильнике = in the fridge
• в холодильник = into the fridge

Russian uses different cases for location and direction:

• в + prepositional for location: where?
• в + accusative for movement into something: where to?

Compare:

• Сырок лежал в холодильнике. = The snack was in the fridge.
• Я положил сырок в холодильник. = I put the snack into the fridge.

The preposition до takes the genitive case.

So:

• вечер = evening
• до вечера = until evening

This phrase means the snack remained there up to the evening.

Other examples:

• до утра = until morning
• до дома = as far as the house / up to the house
• до конца = until the end

This is a question of aspect, which is very important in Russian.

• есть / ел = imperfective, focuses on the process of eating
• съесть / съел = perfective, focuses on the completed result

So брат съел его means the brother ate it up / finished it.

If you said брат ел его, that would sound more like:

• he was eating it
• he ate it (process-focused)
• it does not clearly say whether he finished it

In this sentence, the result matters: the snack was in the fridge, and later the brother ate it completely.

Because его is the accusative form of the pronoun он when it means him/it.

Here the cheese snack is the object of the verb съел, so Russian needs the object form:

• он = he/it (subject form)
• его = him/it (object form)

So:

• Он съел его. = He ate it.

You cannot use он here, because он would be the subject, not the object.

That is true for many inanimate nouns, but not for this pronoun.

For an inanimate masculine noun:

• nominative: сырок
• accusative: сырок

So if you repeated the noun, you could say:

• Брат съел сырок.

But pronouns have their own forms:

• nominative: он
• accusative: его

So once the noun is replaced by a pronoun, его is correct.

The preposition после takes the genitive case.

So:

• работа = work
• после работы = after work

This usually means after the workday / after finishing work.

Other examples:

• после урока = after the lesson
• после фильма = after the movie
• после ужина = after dinner

Russian has no articles like English a/an/the.

That means nouns such as брат can mean:

• brother
• a brother
• the brother

The exact meaning comes from context.

In this sentence:

• этот сырок is already specific because этот means this
• брат is understood from context as the brother / his brother / my brother, depending on the situation

Russian usually does not need an article to show that.

Russian word order is fairly flexible, but different orders change the focus or emphasis.

The given sentence is neutral and natural:

• Этот сырок лежал в холодильнике до вечера, и брат съел его после работы.

It presents the information in a straightforward way:

1. where the snack was
2. until when
3. who ate it
4. when that happened

You could also say:

• После работы брат съел его.
  This emphasizes after work more strongly.

• Брат после работы съел его.
  Also natural, with a slightly different rhythm.

So the original order is not the only possible one, but it is a very normal neutral choice.