Tegnap ellenőriztem utoljára az egyenleget.

Yes:

• Tegnap = yesterday
• ellenőriztem = I checked / I verified
• utoljára = for the last time / last
• az = the
• egyenleget = balance in the object form

A very literal gloss would be:

• Tegnap = yesterday
• ellenőriztem = checked-I
• utoljára = for-the-last-time
• az egyenleget = the balance

So the sentence structure is not word-for-word like English, but each part is straightforward once you know the grammar.

The base verb is ellenőrizni, meaning to check / to verify.

In ellenőriztem:

• the verb stem is ellenőriz-
• Hungarian past tense uses a -t- marker
• the ending shows first person singular: I

So ellenőriztem = I checked.

Hungarian usually packs a lot of information into the verb itself, so one word can already tell you:

• tense: past
• person: 1st person
• number: singular

Because Hungarian usually drops subject pronouns when they are clear from the verb ending.

So:

• ellenőriztem already means I checked

You only need én if you want extra emphasis or contrast, for example:

• Én ellenőriztem = I checked it
• implying maybe someone else did not

This is very normal in Hungarian and is one of the first things English speakers notice.

Because egyenleget is the direct object form.

• egyenleg = balance
• egyenleget = balance as the thing being checked

Hungarian usually marks direct objects with -t.

So:

• ellenőriztem az egyenleget = I checked the balance

Also, the article is az rather than a because egyenleg begins with a vowel sound.

• a before consonant sounds
• az before vowel sounds

So:

• az egyenleg
• az egyenleget when it is the object

Not clearly in this particular form.

Hungarian does have indefinite and definite verb conjugation, and az egyenleget is definitely a definite object. However, in the past tense, first person singular, the form is often the same in both conjugations.

So ellenőriztem by itself does not visibly tell you whether the object is definite or indefinite.

That means:

• the sentence does contain a definite object: az egyenleget
• but the verb form ellenőriztem does not make that contrast obvious here

This is a good example of why learners sometimes cannot identify definiteness from the verb alone.

Utoljára most often means for the last time or last.

In this sentence, it suggests that yesterday was the final time the speaker checked the balance.

That is slightly different from simply saying the most recent time. For that idea, Hungarian often prefers legutóbb.

So the rough contrast is:

• utoljára = for the last time / the last time
• legutóbb = most recently / last time in a neutral chronological sense

This is an important nuance for English speakers, because English last can cover both ideas, while Hungarian often separates them more clearly.

Hungarian word order is much more flexible than English word order, and it is strongly influenced by topic and focus.

Here, Tegnap at the beginning sets the time frame: Yesterday...

Then the sentence gives the action:

• ellenőriztem = I checked
• utoljára = for the last time
• az egyenleget = the balance

So this word order is natural, but it is not the only possible one.

A key idea for learners is:

• English word order mostly shows grammatical roles
• Hungarian endings show grammatical roles, so word order is freer and often shows emphasis

Yes, but the emphasis may change.

For example:

• Utoljára tegnap ellenőriztem az egyenleget.
  = The last time I checked the balance was yesterday.

This version puts more emphasis on when the last checking happened.

• Tegnap utoljára ellenőriztem az egyenleget.
  This is also possible, and keeps yesterday prominent while placing utoljára closer to the verb phrase.

So the core meaning can stay similar, but Hungarian speakers may hear different shades of emphasis depending on the order.

Yes, it is natural, especially if you mean to verify / check carefully.

But Hungarian also often uses other verbs depending on nuance:

• ellenőrizni = to check, verify, inspect
• megnézni = to look at, check in a more everyday sense

So:

• Tegnap ellenőriztem utoljára az egyenleget.
  sounds a bit more like I checked/verified the balance
• Tegnap néztem meg utoljára az egyenleget.
  sounds more like I last looked at the balance

Both can be natural; the choice depends on whether you want a more careful or more casual meaning.