Ελέγχουμε την προθεσμία ολοκλήρωσης.

Because Ελέγχουμε is the 1st person plural form of the verb ελέγχω (to check / to inspect / to control, depending on context).

The ending -ουμε tells you the subject is we, so Greek does not need a separate word for we unless you want extra emphasis.

• Ελέγχουμε = we check / we are checking
• Εμείς ελέγχουμε = we check (with emphasis on we)

It can mean either one.

In Modern Greek, the present tense often covers both:

• we check
• we are checking

So Ελέγχουμε την προθεσμία ολοκλήρωσης could be understood as:

• We check the completion deadline
• We are checking the completion deadline

The exact meaning depends on context.

Because προθεσμία is the direct object of the verb, so it must be in the accusative case.

The noun is feminine singular:

• η προθεσμία = nominative, the deadline (subject form)
• την προθεσμία = accusative, the deadline (object form)

In this sentence:

• Ελέγχουμε = verb
• την προθεσμία = the thing being checked, so it is the object

That is why Greek uses την, not η.

Ολοκλήρωσης is in the genitive singular and means of completion.

It depends on προθεσμία, so the phrase:

• την προθεσμία ολοκλήρωσης

literally means:

• the deadline of completion

In natural English, that becomes something like:

• the completion deadline
• the deadline for completion

So ολοκλήρωσης tells us what kind of deadline it is.

Because Greek often uses the genitive case instead of a separate word like of.

So:

• προθεσμία ολοκλήρωσης = deadline of completion

English often prefers:

• completion deadline
• deadline for completion

Greek can express that relationship just by changing the form of the noun to the genitive:

• ολοκλήρωση → ολοκλήρωσης

The dictionary forms are:

• ελέγχω = to check / inspect / control
• η προθεσμία = deadline
• η ολοκλήρωση = completion

In the sentence, they appear as:

• Ελέγχουμε = from ελέγχω
• την προθεσμία = accusative of η προθεσμία
• ολοκλήρωσης = genitive of η ολοκλήρωση

A simple breakdown is:

• Ελέγχουμε = we check / we are checking
  Verb, present tense, 1st person plural

• την προθεσμία = the deadline
  Feminine singular accusative, direct object

• ολοκλήρωσης = of completion
  Feminine singular genitive, modifying προθεσμία

So the structure is basically:

[Verb] + [Direct object] + [Genitive modifier]

Yes. Greek word order is more flexible than English because case endings show the grammatical roles.

The neutral order here is:

• Ελέγχουμε την προθεσμία ολοκλήρωσης.

But you may also see:

• Την προθεσμία ολοκλήρωσης ελέγχουμε.

That version gives more emphasis to the completion deadline.

Even though word order can change, the original sentence sounds natural and neutral.

Usually yes, if you mean a specific deadline.

• Ελέγχουμε την προθεσμία ολοκλήρωσης. = We are checking the completion deadline.

If you remove the article:

• Ελέγχουμε προθεσμία ολοκλήρωσης.

that sounds less natural in most ordinary contexts and may suggest a more general, less definite meaning. Greek often uses the definite article more regularly than English does.

A rough pronunciation guide is:

E-LENG-khou-me tin pro-thes-MEE-a o-lo-KLEE-ro-sis

A more careful note:

• Ελέγχουμε → stress on -λέγ-
• προθεσμία → stress on -μία
• ολοκλήρωσης → stress on -κλή-

The γχ in Ελέγχουμε is not pronounced like English gch. It is a Greek consonant cluster, and learners usually just need repeated listening to get comfortable with it.

It sounds neutral to slightly formal.

Words like προθεσμία and ολοκλήρωση are common in:

• business Greek
• administration
• project management
• academic or technical contexts

So this sentence would sound very normal in a workplace or official setting.