Παρά το γεγονός ότι αργεί, συμμετέχει.

It means despite the fact that.

This is a fixed, fairly formal way to introduce a contrast. In this sentence:

Παρά το γεγονός ότι αργεί, συμμετέχει.
= Despite the fact that he/she is late, he/she participates.

A more natural English translation might sometimes be Even though he/she is late, he/she still participates.

Because παρά here is followed by a noun phrase, and γεγονός needs the article:

• παρά = despite / in spite of
• το γεγονός = the fact

So:

• παρά το γεγονός = despite the fact

You should think of it as a set phrase. Greek often uses the article in places where English may or may not.

Ότι means that and introduces the content of the fact:

• το γεγονός ότι αργεί = the fact that he/she is late

So the structure is:

• παρά
  • το γεγονός
    • ότι-clause

Literally:
despite the fact that he/she is late

Do not confuse this ότι with ό,τι:

• ότι = that
• ό,τι = whatever

Here it is definitely ότι.

Αργεί comes from αργώ, which commonly means to be late.

So here:

• αργεί = he/she is late

It is:

• 3rd person singular
• present tense
• active voice

Depending on context, it could also sometimes mean is delayed or takes a long time, but in this sentence is late is the natural meaning.

Greek often leaves subject pronouns out because the verb ending already shows the person and number.

Both verbs here are 3rd person singular:

• αργεί = he/she/it is late
• συμμετέχει = he/she/it participates

So Greek does not need to say αυτός / αυτή unless there is special emphasis or a need to clarify who is being talked about.

In this sentence, the subject is understood from context.

Συμμετέχει comes from συμμετέχω, meaning to participate / take part.

Here it stands on its own:

• συμμετέχει = he/she participates

Very often, if you want to say what someone is participating in, Greek uses σε + accusative:

• συμμετέχει στη συζήτηση = he/she participates in the discussion
• συμμετέχει στο μάθημα = he/she takes part in the class

But in your sentence, no object is needed because the point is simply that the person participates.

The comma separates the introductory subordinate clause from the main clause.

• Παρά το γεγονός ότι αργεί = subordinate concessive phrase
• συμμετέχει = main clause

This is similar to English:

• Although he is late, he participates.

Greek commonly uses a comma here when the contrast clause comes first.

Yes, it is understandable and correct, but παρά το γεγονός ότι sounds somewhat formal or written.

In everyday speech, Greek speakers often prefer shorter alternatives such as:

• Αν και αργεί, συμμετέχει. = Although he/she is late, he/she participates.
• Παρόλο που αργεί, συμμετέχει. = Even though he/she is late, he/she participates.

So your original sentence is good Greek, but it has a slightly more formal tone.

Yes. Greek word order is flexible.

You could also say:

• Συμμετέχει, παρά το γεγονός ότι αργεί.

This still means the same thing, but the emphasis shifts a little. Starting with Παρά το γεγονός ότι αργεί foregrounds the contrast first. Starting with Συμμετέχει puts the main action first.

Both are grammatical.

Because the sentence describes a present or general situation:

• αργεί = is late
• συμμετέχει = participates / is participating

Greek present tense can express:

1. something happening now
2. something habitual or generally true

So depending on context, this could mean either:

• Even though he/she is late right now, he/she is participating or
• Even though he/she tends to be late, he/she does participate

Yes. The sentence expresses concession: one fact might make you expect the opposite result, but that expectation is not fulfilled.

You might expect:

• If someone is late, maybe they will not participate

But instead Greek says:

• Παρά το γεγονός ότι αργεί, συμμετέχει.

So the force is:

• Even though this negative condition exists, the main action still happens.

That contrast is the key idea of the sentence.