Χίλια ευρώ είναι πολλά χρήματα.

Because ευρώ is a neuter noun, and χίλια is the neuter plural form used with it.

Greek numerals like χίλιοι / χίλιες / χίλια can agree with the noun they describe:

• χίλιοι άνθρωποι = a thousand people (masculine)
• χίλιες λέξεις = a thousand words (feminine)
• χίλια ευρώ = a thousand euros (neuter)

So in this sentence, χίλια matches ευρώ.

No. ευρώ is normally treated as indeclinable in Modern Greek, so it keeps the same form in singular and plural.

Examples:

• ένα ευρώ = one euro
• δύο ευρώ = two euros
• χίλια ευρώ = one thousand euros

What changes is the article, if there is one:

• το ευρώ = the euro
• τα ευρώ = the euros

In Greek, the usual word for money is χρήματα, which is plural in form.

So Greek often says:

• Έχω χρήματα. = I have money.
• Δεν έχω χρήματα. = I don’t have money.

Even though English uses money as an uncountable singular noun, Greek commonly uses the plural χρήματα for the same idea.

Because χρήματα is neuter plural, and the adjective has to agree with it.

The adjective πολύς changes form:

• πολύς = masculine
• πολλή = feminine
• πολύ = neuter singular
• πολλά = neuter plural

Since χρήματα is neuter plural, the correct form is πολλά.

So:

• πολλά χρήματα = a lot of money

You may also hear πολύ χρήμα, which is another valid way to say a lot of money, but that is a different structure.

It can be either. In the present tense, Greek uses είναι for both:

• he/she/it is
• they are

So είναι does not tell you by itself whether the subject is singular or plural. You understand it from context.

In this sentence, English normally says is:
A thousand euros is a lot of money.

Greek still uses είναι, which works perfectly here.

Because the sentence is talking about the amount in a general way, not about something specific already mentioned.

• Χίλια ευρώ = one thousand euros
• πολλά χρήματα = a lot of money

If you say τα χίλια ευρώ, that usually means the thousand euros, referring to a specific amount already known in the conversation.

So:

• Χίλια ευρώ είναι πολλά χρήματα. = One thousand euros is a lot of money.
• Τα χίλια ευρώ είναι πολλά χρήματα. = The thousand euros are/is a lot of money.
  (more specific, context-dependent)

In this sentence, both main noun phrases are understood as nominative:

• χίλια ευρώ = the subject
• πολλά χρήματα = the complement after είναι

So the structure is basically:

[subject] + [to be] + [predicate/complement]

A small complication: with neuter plural nouns, nominative and accusative often look the same, so the form itself does not always show the case clearly. You understand it from the sentence structure.

Yes. μία χιλιάδα ευρώ is correct and means the same thing.

But χίλια ευρώ is the more natural and common everyday way to say one thousand euros.

So both are possible:

• χίλια ευρώ
• μία χιλιάδα ευρώ

The first is usually simpler and more typical in ordinary speech.

Yes, Greek word order is fairly flexible, but the given order is the most neutral and natural here:

Χίλια ευρώ είναι πολλά χρήματα.

It presents the amount first, then comments on it.

You could also hear:

• Χίλια ευρώ είναι πολλά. = A thousand euros is a lot.
  (χρήματα is left understood)

Changing word order usually changes emphasis, not the basic meaning.

A good pronunciation guide is:

• χίλια = /ˈçi.ʎa/
• ευρώ = /evˈro/
• είναι = /ˈi.ne/
• πολλά = /poˈla/
• χρήματα = /ˈxri.ma.ta/

A few useful notes:

• ευ in ευρώ is pronounced ev here, because the next sound is voiced.
• χ in χίλια is the softer sound /ç/, because it comes before ι.
• χ in χρήματα is the harder /x/ sound.

So the whole sentence is approximately:

/ˈçi.ʎa evˈro ˈi.ne poˈla ˈxri.ma.ta/

More or less, yes—literally it is plural in form, so it can look like many monies to an English speaker.

But you should not translate it word-for-word in normal English. Idiomatically, it just means:

• a lot of money
• a large amount of money

This is a good example of where Greek and English package the same idea differently.