Акт согласования подписали вчера.

Because акт согласования is not the subject. It is the direct object: it is the thing that was signed.

The verb подписали has an implied subject: they / someone / the relevant people signed it. Russian often uses a 3rd person plural verb with no stated subject when the doer is unknown, unimportant, or simply not being named.

So the structure is basically:

• (They) signed — подписали
• the approval document / act — акт согласования
• yesterday — вчера

Russian often omits subject pronouns, especially when they are easy to understand from context.

In this sentence, leaving out они is very natural. In fact, adding они would usually sound more specific, as if you mean a particular group already being discussed.

So:

• Подписали вчера = They / someone signed it yesterday
• Они подписали вчера = They signed it yesterday, with more emphasis on they

Here the sentence has an indefinite-personal feel: the action happened, but the people are not being named.

Yes. Even though the Russian sentence is grammatically active, English will often translate it more naturally as a passive:

• The approval document was signed yesterday

Russian commonly uses this active 3rd person plural pattern where English prefers a passive.

So these are close in meaning:

• Акт согласования подписали вчера.
• Акт согласования был подписан вчера.

The first version is often a bit more natural and lighter in Russian when the agent is unspecified.

The whole phrase functions as the direct object, so it is in the accusative.

However, акт is a masculine inanimate singular noun, and for that type of noun:

• nominative = акт
• accusative = акт

So it looks the same as the dictionary form.

That is why you do not see a visible ending change on акт.

Because Russian often uses a noun + noun in the genitive where English uses of or a noun modifier.

So:

• акт согласования = roughly act/document of approval / coordination

Here согласования answers the question акт чего? — an act/document of what?
Answer: согласования.

This is a very common pattern in Russian:

• центр города — the center of the city
• план проекта — the plan of the project
• акт согласования — the approval/co-ordination document

Because the sentence describes a completed action: the document got signed.

• подписали = signed, as a finished event
• подписывали = were signing / used to sign / signed repeatedly, depending on context

With вчера and a single finished event, подписали is the natural choice.

If you said подписывали, it would suggest something different, for example:

• the process was going on yesterday
• the action was repeated
• the result is not the main point

Yes, the word order can change. Russian word order is flexible, and different orders shift the focus slightly.

Акт согласования подписали вчера puts the document first, then the action, then the time. This can sound like:

• As for the approval document, it was signed yesterday
• or it may put a little extra attention on yesterday

Other possible orders:

• Вчера подписали акт согласования — more neutral if you want to start with the time
• Акт согласования вчера подписали — also possible, with a slightly different rhythm/focus

So the sentence is not just about grammar; word order also helps shape emphasis.

In form, подписали is just the plural past tense, so it can be used with both:

• мы подписали — we signed
• они подписали — they signed

But without a pronoun, the default interpretation in a sentence like this is usually they / someone signed, not we signed.

If you want to clearly mean we, it is safer to say:

• Мы подписали акт согласования вчера

So although the form itself does not show person, the no-pronoun version usually pushes the listener toward an indefinite they reading.

Yes, very much so. Акт in this kind of sentence usually refers to a formal document, not an everyday action or performance.

So the whole sentence sounds like official, business, legal, or administrative Russian.

That is also why the style подписали вчера works well here: it sounds like reporting a document-handling event, not casual conversation.

The main stresses are:

• Акт согласовАния подписАли вчерА

A few notes:

• акт — one syllable, so it is automatically stressed
• согласовАния — stress on ВА
• подписАли — stress on СА
• вчерА — stress on the last syllable

As usual in Russian, unstressed vowels are reduced in pronunciation, so the written form and spoken form are not always identical.