Η εξουσία έχει ευθύνη.

No. In Greek, Η here is the feminine singular definite article, meaning the.

Even though the capital Greek letter Η looks like the English H, in Modern Greek it is pronounced ee, not h. So Η εξουσία is pronounced roughly ee ex-oo-SEE-a.

So at the start of this sentence, Η is just the word the, not an h sound.

Because εξουσία is a feminine singular noun.

Greek definite articles change according to gender, number, and case:

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

Since εξουσία is feminine, it takes η in the nominative singular:

• η εξουσία

A native English speaker often has to get used to this, because English uses just the for everything.

One strong clue is the ending -ία. Many Greek nouns ending in -ία are feminine.

So:

• η εξουσία
• η ιστορία
• η κοινωνία

This is not an absolute rule for every word in Greek, but it is a very common pattern and a useful one to learn.

Έχει is the 3rd person singular present tense of έχω, meaning to have.

So the verb pattern is:

• έχω = I have
• έχεις = you have
• έχει = he/she/it has

Here the subject is η εξουσία, which is singular, so Greek uses έχει.

This is completely normal Greek grammar:

• Η εξουσία έχει... = Authority has...

Greek often leaves off the article with an abstract noun when speaking in a general sense.

So:

• έχει ευθύνη = has responsibility / bears responsibility

If you add the article:

• έχει την ευθύνη

that usually sounds more specific, like:

• has the responsibility
• has the responsibility for it
• holds the specific responsibility

So the version without the article is natural if the idea is general or broad.

Here ευθύνη is the direct object of έχει, so it is in the accusative case.

That can be confusing, because for many feminine nouns like this one, the noun itself looks the same in the nominative and accusative singular:

• nominative: η ευθύνη
• accusative: την ευθύνη

Notice that the article changes, but the noun ευθύνη itself stays the same in form.

In this sentence there is no article before ευθύνη, so you identify it as the object mainly from:

• the verb έχει
• the sentence structure
• the meaning

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

The basic order here is:

• Η εξουσία έχει ευθύνη.

That is a straightforward subject–verb–object order.

But Greek can move things around for emphasis. For example:

• Ευθύνη έχει η εξουσία.
• Η εξουσία ευθύνη έχει.
  This sounds more marked or rhetorical.

The original sentence is the most neutral and natural choice for a learner to start with.

A rough pronunciation is:

ee ex-oo-SEE-a EH-khee ef-THEE-nee

A slightly more careful breakdown:

• Η = ee
• εξουσία = ek-soo-SEE-a
• έχει = EH-khee or EH-hee, depending on accent and speaking style
• ευθύνη = ef-THEE-nee

The accent marks show which syllable gets the stress:

• εξουσία
• έχει
• ευθύνη

It can mean several related things, depending on context, such as:

• authority
• power
• the authorities
• governmental power
• control

So η εξουσία can refer to:

• authority in a general sense
• those in power
• political power
• the ruling power

That is why context matters. In this sentence, the idea is that whoever holds power or authority also bears responsibility.

Yes, but the wording is slightly different.

• Η εξουσία έχει ευθύνη.
  = authority has responsibility / bears responsibility

• Η εξουσία είναι υπεύθυνη.
  = authority is responsible

These are close in meaning, but not identical in tone:

• έχει ευθύνη focuses on possessing or bearing responsibility
• είναι υπεύθυνη describes the subject as responsible

Both are natural Greek, but the original sentence uses the very common pattern έχω ευθύνη.

You would usually add the article:

• Η εξουσία έχει την ευθύνη.

That sounds more like:

• The authority has the responsibility
• The authority bears the responsibility

You could also make it even more specific with extra words, for example:

• Η εξουσία έχει την ευθύνη για αυτό.
  = The authority has responsibility for this.

So the difference is:

• ευθύνη = responsibility in a general sense
• την ευθύνη = the responsibility, a more definite or specific one