Το δίπλωμα οδήγησης είναι εδώ.

A natural breakdown is:

• Το = the (neuter singular article)
• δίπλωμα = license / diploma / certificate
• οδήγησης = of driving
• είναι = is
• εδώ = here

Grammatically:

• Το δίπλωμα οδήγησης is the subject: the driver’s license
• είναι is the verb: is
• εδώ is an adverb of place: here

So the structure is basically:

[The driver’s license] [is] [here].

Yes, but this is a bit of a false friend.

In Greek, δίπλωμα can mean:

• a diploma / certificate
• a license, especially in everyday speech for a driver’s license

So in this sentence, δίπλωμα does not mean an academic diploma. It means a license, specifically a driver’s license because of οδήγησης.

A very close literal idea is:

• δίπλωμα = license/certificate
• δίπλωμα οδήγησης = driving license / driver’s license

δίπλωμα is a neuter noun in Greek, so it takes the neuter singular article το.

That is why you get:

• το δίπλωμα

not:

• ο δίπλωμα
• η δίπλωμα

Many Greek neuter nouns end in -μα, and δίπλωμα is one of them.

Because Greek uses the genitive here.

The basic noun is:

• η οδήγηση = driving

Its genitive singular form is:

• της οδήγησης = of driving

In the phrase δίπλωμα οδήγησης, the second noun works like of driving, so the whole phrase literally means:

• license of driving

which English expresses as:

• driver’s license
• driving license

So οδήγησης is the genitive singular of οδήγηση.

Because in this kind of noun phrase, Greek often leaves out the article before the genitive noun when it is giving the type or function of the first noun.

So:

• δίπλωμα οδήγησης = driving license / driver’s license

This is like a fixed combination.

If you said το δίπλωμα της οδήγησης, it would sound different and less natural here. It would suggest something more literal like the diploma/certificate of the driving, not the normal everyday phrase for a driver’s license.

Yes, it is very common in everyday Greek.

You may also see:

• άδεια οδήγησης

This is a bit more official and corresponds closely to driving permit / driving license.

So in practice:

• δίπλωμα οδήγησης = very common in speech
• άδεια οδήγησης = also correct, often more official

Yes. Greek word order is more flexible than English.

These are all possible:

• Το δίπλωμα οδήγησης είναι εδώ.
• Εδώ είναι το δίπλωμα οδήγησης.
• Το δίπλωμα οδήγησης εδώ είναι. — possible, but much less neutral

The most neutral version is the original:

• Το δίπλωμα οδήγησης είναι εδώ.

If you put εδώ first, you often emphasize here:

• Εδώ είναι το δίπλωμα οδήγησης. = The driver’s license is here.

Usually, no, not in a normal full sentence like this.

Greek generally keeps the present tense of to be in statements such as:

• Το δίπλωμα οδήγησης είναι εδώ.

If you drop είναι and say:

• Το δίπλωμα οδήγησης εδώ

it sounds incomplete in most contexts, like a note, a label, or very broken speech.

So for normal spoken and written Greek, keep είναι.

A rough pronunciation guide is:

• to DHEE-plo-ma o-THEE-yi-sis EE-ne e-THO

A few useful notes:

• δίπλωμα is stressed on δί-
• οδήγησης is stressed on δή-
• είναι is stressed on εί-
• εδώ is stressed on the second syllable: -δώ

Also:

• δ sounds like the th in this
• γ before η / ι has a soft sound, a bit like y in this word

So οδήγησης does not sound like it is written in English.

The noun cases are:

• το δίπλωμα = nominative singular neuter
  It is the subject of the sentence.

• οδήγησης = genitive singular feminine
  It depends on δίπλωμα and means of driving.

So the phrase is built as:

• nominative noun + genitive noun

which is a very common Greek pattern:

• φλιτζάνι καφέ = cup of coffee
• ζώνη ασφαλείας = seat belt
• δίπλωμα οδήγησης = driver’s license

Usually yes, but like many adverbs, its exact feel depends on context.

In this sentence:

• εδώ simply means here, meaning in this place

Examples:

• Το βιβλίο είναι εδώ. = The book is here.
• Έλα εδώ. = Come here.

So in your sentence, εδώ is straightforward and natural.