Η αμοιβή είναι δίκαιη.

No. In Greek, Η here is the capital form of η, and in this sentence it is the feminine singular definite article: the.

So:

• η = the for feminine singular nouns
• Η is just capitalized because it begins the sentence

It is pronounced ee, not like the English h sound.

Because αμοιβή is a feminine noun, and Greek articles must agree with the noun’s gender.

The basic singular definite articles are:

• ο = masculine the
• η = feminine the
• το = neuter the

Since αμοιβή is feminine, the correct article is η:

• η αμοιβή

In this sentence, you can tell from two things:

1. it takes the feminine article η
2. it takes the feminine adjective form δίκαιη

So the sentence itself gives you the clue.

Also, many nouns ending in -ή are feminine, although you should still learn nouns with their article when possible:

• η αμοιβή
• η ζωή
• η φωνή

A very good habit is to memorize new nouns together with the article, not alone.

Because είμαι means I am, while είναι means he/she/it is or they are.

Here the subject is η αμοιβή = the compensation/pay, which is a third-person singular noun, so Greek uses είναι:

• εγώ είμαι = I am
• η αμοιβή είναι = the compensation is

So είναι is exactly the right form here.

Because adjectives in Greek must agree with the noun they describe in gender, number, and case.

Here, αμοιβή is:

• feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• masculine: δίκαιος
• feminine: δίκαιη
• neuter: δίκαιο

That is why Greek says:

• Η αμοιβή είναι δίκαιη.

Compare:

• Ο μισθός είναι δίκαιος. = masculine
• Το ποσό είναι δίκαιο. = neuter

In normal standard Greek, you would usually keep the article: Η αμοιβή είναι δίκαιη.

Greek often uses the definite article in places where English may or may not use the. Without the article, Αμοιβή είναι δίκαιη sounds unnatural in ordinary speech.

So for a learner, the safe and natural version is:

• Η αμοιβή είναι δίκαιη.

Not exactly.

αμοιβή is a fairly broad word. It can mean things like:

• compensation
• remuneration
• pay
• fee
• reward

Depending on context.

By contrast:

• μισθός usually means salary or wage
• πληρωμή means payment

So αμοιβή is a bit more general than μισθός. In this sentence, it sounds like the compensation/pay is fair.

Yes, Greek word order is more flexible than English, but the original sentence is the most neutral and straightforward:

• Η αμοιβή είναι δίκαιη.

If you change the order, you change the emphasis. For example:

• Δίκαιη είναι η αμοιβή.

This puts more focus on δίκαιη = fair.

So yes, other orders are possible, but the original is the best default pattern for learners.

Yes, the accent marks matter because they show which syllable is stressed.

Roughly:

• Η → ee
• αμοιβή → a-mi-VEE
• είναι → EE-ne
• δίκαιη → roughly THEE-keh-ee (with th as in this)

So the whole sentence is roughly:

• ee a-mi-VEE EE-ne THEE-keh-ee

The written accents show the stress:

• αμοιβή → stress on the last syllable
• είναι → stress on the first syllable
• δίκαιη → stress on the first syllable

The article η normally has no accent.

Because in this sentence δίκαιη is a predicate adjective, not an adjective directly attached before the noun.

English works the same way:

• The pay is fair.

Here fair comes after is.

Greek does the same:

• Η αμοιβή είναι δίκαιη.

If you wanted the adjective directly with the noun, you would get a structure like:

• η δίκαιη αμοιβή = the fair compensation

So:

• η δίκαιη αμοιβή = adjective directly modifying the noun
• η αμοιβή είναι δίκαιη = adjective used after is