Я долго искал ценник на чай и заметил, что на него действует акция.

Ценник means the physical price tag / price label you see in a store.

• цена = the price itself
• ценник = the tag/sign showing the price

So я искал ценник means I was looking for the price tag, not just thinking about the price in the abstract.

In shop language, ценник на X means the price tag for X.

So:

• ценник на чай = the price tag for tea
• ценник на хлеб = the price tag for bread
• ценник на молоко = the price tag for milk

This на is very common in Russian retail speech. It does not mean the tag is physically sitting on the tea. It means the tag belongs to / refers to that product.

Because after на in ценник на чай, the noun is in the accusative case.

For inanimate masculine nouns, the accusative often looks exactly like the nominative:

• nominative: чай
• accusative: чай

So the case did change in function, but the form stayed the same.

If the noun were feminine, you would often see the change more clearly:

• ценник на воду
• ценник на рыбу

In the Russian past tense, verbs agree with the speaker’s gender in the singular.

So:

• Я долго искал = I was looking for a long time if the speaker is male
• Я долго искала = same meaning, but the speaker is female

Likewise:

• заметил = male speaker
• заметила = female speaker

This is normal in Russian and happens with past-tense verbs.

This is a very typical aspect choice in Russian.

• искал is imperfective: it describes an ongoing process or duration
  
  • I was searching / I kept looking
• заметил is perfective: it describes a completed event, a moment of noticing
  
  • I noticed

So the sentence presents:

1. a process: I was searching for a while
2. a single result/event: then I noticed

That combination is very natural.

Yes. Долго means for a long time / for quite a while.

So Я долго искал... means:

• I looked for it for a long time
• I was searching for it for quite a while

It often goes especially well with the imperfective verb, because imperfective verbs are good at showing duration and process.

Because что introduces a subordinate clause.

Main clause:

• Я долго искал ценник на чай и заметил

Subordinate clause:

• что на него действует акция

Russian normally puts a comma before что in this kind of sentence, just like English often separates that-clauses in writing structure, though English punctuation works differently.

Literally, акция действует means something like a promotion is in effect / is valid / applies.

In stores, акция usually means:

• promotion
• special offer
• sale deal

So на него действует акция means there is a promotion applying to it.

This is more specific than simply saying есть акция:

• есть акция = there is a promotion
• действует акция = the promotion is currently valid / applies

Because Russian uses the fixed pattern:

• на что действует акция
• на что действует скидка

This means a promotion/discount applies to what?

So:

• на чай действует акция
• на этот товар действует скидка
• на него действует акция

Here на takes the accusative, and него is the accusative form of он after a preposition.

So this is not a literal spatial on. It is just the normal Russian construction for applies to in this context.

Grammatically, него could seem a little ambiguous, because both чай and ценник are masculine nouns.

But in meaning, it clearly refers to чай, because a promotion normally applies to the product, not to the price tag.

So the intended sense is:

• I was looking for the price tag for the tea and noticed that the tea was on promotion

If you want to remove all ambiguity, Russian could say:

• ...и заметил, что на чай действует акция

That is more explicit.

No. This is a very important false friend.

In this sentence, акция means:

• promotion
• special offer
• sales campaign

It does not mean ordinary English action.

Depending on context, акция can also mean things like a public event or campaign, but in store language it very often means promotion.

Yes, that is grammatically possible. Russian word order is flexible.

Compare:

• что на него действует акция
• что акция действует на него

Both can work, but they feel slightly different in emphasis.

In the original sentence, на него comes first inside the clause, which helps highlight the item the promotion applies to. It sounds very natural in this shopping context.

So the original word order is not strange; it is a normal Russian way to present the information.