Таможенник посмотрел на мой чемодан и спросил, везу ли я что-нибудь хрупкое.

Посмотрел is the perfective past form of посмотреть, so it presents the action as a single completed event: the customs officer looked at the suitcase.

If you used смотрел, that would be imperfective and would sound more like was looking, looked for a while, or used to look, depending on context.

So here:

• Таможенник посмотрел... = the officer took a look
• Таможенник смотрел... = the officer was looking / kept looking

The perfective fits well because the sentence describes a sequence of completed actions:

1. he looked,
2. then he asked.

After смотреть / посмотреть, Russian normally uses на + accusative:

• смотреть на кого? что?
• посмотреть на кого? что?

So:

• на мой чемодан = at my suitcase

Here чемодан is masculine inanimate singular, and in the accusative that looks the same as the nominative:

• nominative: мой чемодан
• accusative: мой чемодан

So even though the form looks unchanged, it is accusative because the verb requires it.

For the same reason as посмотрел: спросил is perfective and means he asked once, as a completed action.

• спросил = asked (one completed question)
• спрашивал = was asking / asked repeatedly / used to ask

In this sentence, the officer asks one question at one moment, so perfective спросил is the natural choice.

The particle ли is used to form an indirect yes/no question, often equivalent to English whether or if.

So:

• спросил, везу ли я... = asked whether I was carrying...

The basic direct question would be something like:

• Вы везёте что-нибудь хрупкое? = Are you carrying anything fragile?

In indirect speech, Russian often uses ли:

• Он спросил, везу ли я что-нибудь хрупкое.
• literally: He asked, am-carrying whether I something fragile.
• natural English: He asked whether I was carrying anything fragile.

Ли usually comes after the word that is being focused or highlighted.

In везу ли я, the focus is on the action am carrying. The officer is asking whether I am carrying anything fragile.

So:

• везу ли я... = whether I am carrying...
• я ли везу... would mean something more like whether it is I who am carrying..., which is a different emphasis

This is a very common pattern in Russian indirect questions:

• Он спросил, знаю ли я.
• Она поинтересовалась, придёт ли он.

Russian does not do the same kind of tense backshifting that English often does.

English often says:

• He asked whether I was carrying...

But Russian keeps the tense that fits the situation from the speaker’s point of view in the original question:

• везу ли я = whether I am carrying / whether I’m bringing

This is normal in Russian indirect speech.

Compare:

• Он сказал, что живёт в Москве. = He said that he lives/lived in Moscow.
• Она спросила, знаю ли я это. = She asked whether I knew it.

So спросил in the past + везу in the present is completely standard.

Что-нибудь is very common in questions, conditional contexts, and statements involving uncertainty or non-specificity.

Here the customs officer is asking whether there is anything at all fragile, without having a specific item in mind. That makes что-нибудь very natural.

A rough comparison:

• что-то = something
• что-нибудь = anything / something-or-other

In yes/no questions after ли, что-нибудь is especially common:

• Есть ли у вас что-нибудь для декларирования?
• Везёте ли вы что-нибудь хрупкое?

So in this sentence, что-нибудь sounds more idiomatic than что-то.

Хрупкое is neuter singular because it agrees with the implied noun behind что-нибудь.

Since что-нибудь is an indefinite pronoun meaning something / anything, an adjective describing it often appears in the neuter singular:

• что-нибудь интересное = anything interesting
• что-то странное = something strange
• ничего важного = nothing important
• что-нибудь хрупкое = anything fragile

So хрупкое is not modifying чемодан. It is modifying что-нибудь.

Yes. This is very common in Russian.

An adjective can function almost like a noun when the noun is understood from context. Here:

• что-нибудь хрупкое literally means something fragile
• the noun is not stated separately; the adjective carries the descriptive meaning by itself

This happens a lot in Russian:

• что-то новое = something new
• всё хорошее = everything good
• ничего странного = nothing strange

So хрупкое is perfectly normal here.

Везти usually means to transport, to take, to bring, often with the idea of moving something from one place to another, frequently by vehicle.

In customs or travel contexts, it is often used where English says carry, bring, or have with you:

• Что вы везёте? = What are you bringing/carrying?
• Я везу подарки. = I’m bringing gifts.

So in this sentence, везу ли я что-нибудь хрупкое is naturally translated as whether I was carrying anything fragile, even though the core Russian verb is closer to transport / bring along.

Yes, Russian word order is flexible, but different orders change emphasis.

The given version is very natural:

• ...спросил, везу ли я что-нибудь хрупкое.

Other possibilities can exist, but they may sound marked or shift the focus:

• ...спросил, я везу ли что-нибудь хрупкое — awkward/unusual
• ...спросил, не везу ли я что-нибудь хрупкое — could sound more tentative/polite in some contexts

So the original order is the standard one for an indirect yes/no question with ли.

Because везу ли я что-нибудь хрупкое is a subordinate clause attached to спросил.

Russian writes a comma before subordinate clauses very consistently:

• Он сказал, что устал.
• Она спросила, приду ли я.
• Таможенник... спросил, везу ли я что-нибудь хрупкое.

So the comma marks the start of the indirect question.