Παρεμπιπτόντως, το γραφείο είναι ανοιχτό.

Παρεμπιπτόντως means by the way or incidentally.

It is correct and natural Greek, but it can sound a little more formal or bookish than everyday English by the way. You will still hear or read it, but in very casual conversation people may also use simpler ways to add an extra point.

In this sentence, it works like a discourse marker: it introduces an extra piece of information.

Because Παρεμπιπτόντως is being used as a parenthetical opening word, similar to By the way, ... in English.

So the comma separates the introductory comment from the main statement:

• Παρεμπιπτόντως, = By the way,
• το γραφείο είναι ανοιχτό. = the main sentence

In informal writing, punctuation can sometimes be looser, but the comma here is standard.

A rough pronunciation is:

Παρεμπιπτόντως, το γραφείο είναι ανοιχτό.
pa-rem-bi-PTON-dos, to ghra-FEE-o EE-ne a-nee-HTO

A few helpful notes:

• The stress is shown by the written accent marks:
  • Παρεμπιπτόντως
  • γραφείο
  • ανοιχτό
• μπ inside a word often sounds like b or mb
• γρ in γραφείο starts with a soft Greek γ, not a hard English g
• χ in ανοιχτό is the throaty sound heard in German Bach or Scottish loch

So the pronunciation above is only an approximation for English speakers.

Γραφείο is a neuter noun, so it takes the neuter singular article το.

That is why you get:

• το γραφείο = the office

This is something you have to learn with the noun: in Greek, nouns have grammatical gender, and the article must match it.

Also, many nouns ending in -είο are neuter, so that ending is a useful clue.

It can mean office, and in some contexts it can also mean desk.

In this sentence, office is the natural meaning, because is open fits an office very well:

• Το γραφείο είναι ανοιχτό = The office is open

If you were talking about a piece of furniture, context would normally make that clear.

Because ανοιχτός is an adjective, and Greek adjectives must agree with the noun they describe in gender and number.

The forms are:

• ανοιχτός = masculine
• ανοιχτή = feminine
• ανοιχτό = neuter

Since γραφείο is neuter singular, the adjective must also be neuter singular:

• το γραφείο είναι ανοιχτό

Compare:

• ο δρόμος είναι ανοιχτός = the road is open
• η πόρτα είναι ανοιχτή = the door is open
• το γραφείο είναι ανοιχτό = the office is open

Yes. Ανοιχτό and ανοικτό are both standard.

In everyday Modern Greek, ανοιχτό is very common in speech. Ανοικτό can sound a bit more formal or more typical of written language in some contexts.

So both of these are acceptable:

• Το γραφείο είναι ανοιχτό
• Το γραφείο είναι ανοικτό

Είναι is the verb is.

More specifically, it is the 3rd person singular form of είμαι = to be.

So the structure is:

• το γραφείο = the office
• είναι = is
• ανοιχτό = open

Greek normally keeps the verb to be in a sentence like this, so είναι is not optional in normal speech.

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

The most neutral version here is:

• Παρεμπιπτόντως, το γραφείο είναι ανοιχτό.

But other orders are possible depending on emphasis, for example:

• Το γραφείο είναι ανοιχτό, παρεμπιπτόντως.

That said, the original sentence is the most straightforward and natural way to say it.

In normal Greek, you would usually keep the article:

• το γραφείο είναι ανοιχτό

Greek uses the definite article much more regularly than English in many situations, and with a noun like γραφείο in this sentence, leaving it out would sound unnatural unless you were speaking in a very special style, such as notes, headlines, or very telegraphic speech.

So for a learner, the safe choice is:

• το γραφείο = the office