Ο συνεργάτης μου που μένει κοντά στο γραφείο έρχεται πάντα νωρίς.

In Greek, a possessive like μου usually does not replace the definite article. So:

• ο συνεργάτης μου = my colleague
• literally, it looks more like the colleague of mine

The article ο agrees with the noun συνεργάτης and shows that it is masculine, singular, nominative.

Because μου here is a weak possessive pronoun (historically/genetically the genitive form of εγώ), and in normal Greek it usually comes after the noun:

• ο φίλος μου = my friend
• το σπίτι μου = my house
• ο συνεργάτης μου = my colleague

So this word order is completely standard.

Here που introduces a relative clause and means who / that:

• ο συνεργάτης μου που μένει κοντά στο γραφείο = my colleague who lives near the office

In everyday Modern Greek, που is the most common relative word. Unlike English who / which / that, it does not change form for gender or number.

Because this is a restrictive relative clause: it identifies which colleague you mean.

So the sentence means:

• the colleague of mine who lives near the office
  not
• my colleague, who lives near the office, ...

In both Greek and English, restrictive relative clauses normally do not take a comma.

Yes, you could say something like:

• Ο συνεργάτης μου ο οποίος μένει κοντά στο γραφείο...

But in this sentence, που is much more natural and common in everyday Greek.
ο οποίος sounds more formal, heavier, and is often used when extra clarity is needed.

So for normal speech, που is the best choice here.

Μένει is the 3rd person singular present of μένω.

So:

• μένω = I live / I stay
• μένεις = you live / stay
• μένει = he/she lives / stays

Greek μένω can mean both stay and live, depending on context.
In this sentence, because it talks about where the colleague is based, μένει means lives.

Κοντά means near / close.
It is often followed by σε + article.

Here:

• σε + το = στο
• so κοντά στο γραφείο = near the office

Also, γραφείο is a neuter noun, and after σε Greek uses the accusative.
For neuter nouns like γραφείο, the nominative and accusative singular look the same, so you still see γραφείο.

Έρχεται is the 3rd person singular present of έρχομαι:

• έρχομαι = I come / I am coming
• έρχεται = he/she comes / is coming

This verb has middle/passive-style endings, but its meaning here is active. Greek has several common verbs like this. So even though it looks different from a verb like μένει, it simply means comes.

Because the sentence includes πάντα, the meaning is clearly habitual:

• έρχεται πάντα νωρίς = he always comes early

Both are adverbs:

• πάντα = always
• νωρίς = early

They modify the verb έρχεται:

• έρχεται πάντα νωρίς = comes always early = always comes early

Πάντα tells you how often, and νωρίς tells you when/how early.
Together they give a natural idea of repeated habit.

Greek word order is more flexible than English, but some orders sound more natural than others.

The given sentence:

• Ο συνεργάτης μου που μένει κοντά στο γραφείο έρχεται πάντα νωρίς.

is a very normal, neutral order.

You can move some elements for emphasis, for example:

• Πάντα έρχεται νωρίς ο συνεργάτης μου που μένει κοντά στο γραφείο.

But that sounds more marked and stylistic.
For a learner, the original order is the safest and most natural one to use.