Η απόφαση επί της ένστασης θα είναι έτοιμη αύριο.

Greek uses the definite article much more often than English. In a sentence like this, η απόφαση is the natural way to say the decision.

If you dropped the article and said Απόφαση ... θα είναι έτοιμη αύριο, it would sound unnatural in normal prose unless you were using a headline style or some very special context.

So here:

• η απόφαση = nominative singular, feminine
• it is the subject of the sentence

In this sentence, επί της ένστασης is a formal way to say regarding the objection/appeal or on the objection/appeal.

The preposition επί is quite old and formal in this use. You will often see it in:

• legal language
• official documents
• bureaucratic writing
• formal announcements

So η απόφαση επί της ένστασης means something like the decision on the objection.

Because επί here takes the genitive in formal Greek.

That is why you get:

• της ένστασης = genitive singular
• not την ένσταση or η ένσταση

So the structure is:

• επί
  • genitive
• επί της ένστασης

This is one of those combinations that learners usually just need to memorize.

They are the definite article, but in different cases because they belong to different parts of the sentence.

• η απόφαση: nominative, because it is the subject
• της ένστασης: genitive, because it follows επί

Both nouns are feminine singular, but their role in the sentence is different, so the article changes form.

Θα is the future marker, and είναι is the verb to be.

So:

• είναι = is
• θα είναι = will be

This is the normal way to form the future in Modern Greek:

• θα
  • verb

Here it gives:

• θα είναι έτοιμη = will be ready

Because έτοιμη is an adjective and it must agree with απόφαση, which is feminine singular.

The adjective έτοιμος / έτοιμη / έτοιμο changes form depending on gender and number:

• masculine: έτοιμος
• feminine: έτοιμη
• neuter: έτοιμο

Since απόφαση is feminine, the correct form is έτοιμη.

It is an adjective.

More specifically, it is a predicate adjective after the verb είναι. It describes the subject:

• Η απόφαση ... θα είναι έτοιμη
• The decision ... will be ready

So έτοιμη agrees with απόφαση in gender and number.

Usually not in casual speech. It sounds formal and official.

In everyday Greek, people would more often say something like:

• η απόφαση για την ένσταση
• η απόφαση σχετικά με την ένσταση

Those are less bureaucratic and more conversational.

So this sentence has a distinctly formal, administrative tone.

Yes, Greek word order is more flexible than English word order.

This sentence could also appear as:

• Η απόφαση θα είναι έτοιμη αύριο.
• Η απόφαση για/επί της ένστασης θα είναι έτοιμη αύριο.

But in the original sentence, επί της ένστασης is placed right after απόφαση because it closely defines what kind of decision is meant.

So the original order is very natural, especially in formal writing.

Because αύριο is an adverb meaning tomorrow.

Greek often uses time adverbs directly, just like English:

• σήμερα = today
• αύριο = tomorrow
• χθες = yesterday

So:

• θα είναι έτοιμη αύριο = it will be ready tomorrow

No article or preposition is needed.

Yes, that is a good nuance question.

Θα είναι έτοιμη αύριο literally means will be ready tomorrow. It says the decision will be prepared/available by tomorrow, but it does not necessarily specify:

• whether it will be officially announced tomorrow
• whether it will be delivered tomorrow
• whether it will simply be completed internally by tomorrow

The exact practical meaning depends on context.

A rough pronunciation guide is:

ee a-PO-fa-see e-PEE tees EN-sta-sees tha EE-ne E-toi-mee AV-rio

A more careful breakdown:

• Η απόφαση → ee a-PO-fa-see
• επί της ένστασης → e-PEE tees EN-sta-sees
• θα είναι → tha EE-ne
• έτοιμη → E-toi-mee
• αύριο → AV-rio

A few notes:

• η / ι / υ / ει / οι are all pronounced like ee in Modern Greek
• αι is pronounced like e
• αυ before a voiced sound is often pronounced like av, so αύριο sounds like AV-rio