Θα γράψει, έστω κι αν αργήσει.

It has two parts:

• Θα γράψει = the main clause
• έστω κι αν αργήσει = a concessive clause, meaning something like even if he/she is late

So the sentence means that the action in the main clause will still happen despite the possible problem mentioned in the second clause.

θα γράψει is the simple future:

• θα = future particle
• γράψει = 3rd person singular form of γράφω (to write)

So θα γράψει means:

• he will write
• she will write
• it will write

Greek does not need to state the subject pronoun here.

Also, this future is perfective, so it usually refers to a single complete action: will write rather than will be writing.

Because Greek often leaves out subject pronouns when they are not needed.

The verb form γράψει already tells you that the subject is:

• 3rd person
• singular

So Greek can simply say θα γράψει instead of αυτός/αυτή θα γράψει.

English usually needs he/she/it, but Greek often does not.

έστω κι αν means even if.

It introduces a contrast or concession: the main action is still true despite the condition.

In this sentence:

• Θα γράψει = the writing will happen
• έστω κι αν αργήσει = even if there is lateness / even if he/she is late

A literal breakdown is not very helpful here, because έστω κι αν works as a set expression. You should learn it as a whole meaning even if.

κι is a shortened form of και.

So:

• κι αν
• και αν

are basically the same in meaning here.

Before a vowel, κι is extremely common and sounds more natural and smoother in speech. That is why έστω κι αν is the usual form.

Because after αν Greek does not normally use θα.

So Greek says:

• αν αργήσει = if he/she is late / if he/she ends up being late

not:

• αν θα αργήσει in this kind of sentence

This is an important difference from what English learners sometimes expect. In Greek, after words like αν, you usually use the dependent verb form directly, without θα.

Not by itself.

αργήσει is a form that appears in several environments:

• θα αργήσει = he/she will be late
• να αργήσει = for him/her to be late, to be late
• αν αργήσει = if he/she is late

So the form αργήσει itself is not enough to tell you the meaning. The particle before it matters:

• θα gives a future meaning
• να gives a subjunctive-type meaning
• αν gives an if/conditional meaning

In this sentence, because it is αν αργήσει, it means if he/she is late.

It comes from αργώ, which can mean things like:

• be late
• take too long
• be delayed

In this sentence, the most natural meaning is be late or be delayed.

So έστω κι αν αργήσει means:

• even if he/she is late
• even if there is a delay

The best English wording depends on context.

Because they are both 3rd person singular perfective non-past forms.

Here are the dictionary verbs:

• γράφω → perfective stem gives γράψει
• αργώ → perfective form gives αργήσει

These forms are used after particles like:

• θα
• να
• αν

So in this sentence:

• θα γράψει
• αν αργήσει

both use that same type of verb form, but the particles give them different functions.

Yes, it is natural here.

The comma separates:

• the main clause: Θα γράψει
• the concessive addition: έστω κι αν αργήσει

So the punctuation helps show the sentence structure clearly.

You could also reverse the order:

• Έστω κι αν αργήσει, θα γράψει.

That would also be perfectly natural.

Yes.

ακόμα κι αν is another very common way to say even if.

So these are both possible:

• Θα γράψει, έστω κι αν αργήσει.
• Θα γράψει, ακόμα κι αν αργήσει.

They are very close in meaning.
ακόμα κι αν is often especially common in everyday speech, while έστω κι αν can feel a bit more formal or stylistic depending on context.