На ценнике было написано, что молоко стоит дешевле обычного.

На ценнике uses the preposition на in its location meaning, so it takes the prepositional case.

• ценник = price tag / price label
• на ценнике = on the price tag

This is the normal way to say that some information is physically written on a tag, sign, label, board, etc.

Было написано is an impersonal passive construction.

A useful literal breakdown is:

• было = was
• написано = written

So literally, it is something like it was written.

Russian often uses this kind of structure when English might say:

• it said on the price tag
• it was written on the price tag

Also, написано here is a short passive participle from написать.

Because this is an impersonal sentence: there is no explicitly stated grammatical subject that the verb has to agree with.

In that kind of construction, Russian normally uses the neuter singular form:

• было написано
• было сказано
• было указано

If you added an actual subject, then agreement would change:

• На ценнике был написан текст.
• На ценнике была написана цена.

But in your sentence, there is no expressed noun like текст or цена, so Russian uses the neutral impersonal form было написано.

Because the two verbs describe different things.

• было написано describes the situation in the narration: at that time, that text was on the tag
• стоит is part of the content of what was written: the text itself stated a present fact about the price

So Russian keeps the tense that makes sense inside the reported statement.

This is very normal. Russian does not force a tense backshift the way English sometimes does.

Compare:

• На двери было написано, что магазин закрывается в 8.
• Он сказал, что живёт в Москве.

Even if the reporting verb is in the past, the subordinate clause can stay in the present if that is the intended meaning.

Что introduces a subordinate clause.

So the structure is:

• На ценнике было написано, ...
• что молоко стоит дешевле обычного

The comma is required because Russian separates the main clause from the subordinate clause with a comma.

Here что is basically the connector meaning that.

Because молоко is the subject of стоит.

In this clause:

• молоко стоит дешевле обычного

the thing that costs less is молоко, so it stays in the nominative case.

Also, молоко is a neuter singular noun.

Because this is the verb стоить, not стоять.

There are two different verbs with the same spelling in this form:

• сто́ит = costs, is worth
• стои́т = stands

In writing, context usually makes it clear. Here, because the sentence is about milk and a price tag, стоит clearly means costs.

This is very common Russian:

• Сколько это стоит?
• Молоко стоит дешевле.

Дешевле is the comparative form: cheaper.

It comes from дешёвый / дёшево and is used when comparing price.

After стоить, Russian very naturally uses a comparative:

• стоит дешевле = costs less / is cheaper

So this is the normal pattern for price comparison.

Because Russian comparatives can take the genitive case to express the thing or standard being compared against.

So:

• дешевле обычного

literally means something like:

• cheaper than the usual / than normal / than what is usual

This is a very common Russian pattern:

• старше брата = older than his brother
• лучше прежнего = better than before
• дешевле обычного = cheaper than usual / cheaper than normal

So обычного is genitive because it depends on the comparative дешевле.

Yes. That is a very common alternative.

Both are natural, but there is a small difference in feel:

• дешевле обычного = a bit more compact and condensed
• дешевле, чем обычно = very clear and conversational

In many contexts, they mean nearly the same thing.

So these are both fine:

• Молоко стоит дешевле обычного.
• Молоко стоит дешевле, чем обычно.

You can think of it that way, yes.

Russian often allows an adjective form to stand on its own when the missing idea is understood from context. Here, обычного can feel like a compressed comparison standard.

Depending on context, a learner might imagine something like:

• обычного уровня
• обычной цены
• обычного [для него]
• or simply than usual

In real usage, though, you usually do not need to reconstruct a missing noun. It is best to learn дешевле обычного as a normal comparative expression.

Yes. Russian word order is flexible.

This version:

• На ценнике было написано, что молоко стоит дешевле обычного.

puts на ценнике first, which sets the scene immediately: we are talking about what was written on the price tag.

You could also say:

• Было написано на ценнике, что молоко стоит дешевле обычного.

That is grammatical too, but it sounds a bit less natural in many contexts.

So the original word order is a very normal, neutral choice.