Έστω κι αν αργήσει, θα περιμένουμε.

As a fixed expression, Έστω κι αν means even if or even though in a somewhat formal or literary way.

• έστω by itself originally means something like let it be or granted
• together with κι αν, the whole phrase works as a concessive expression: even if

So in this sentence, you should learn Έστω κι αν as one chunk rather than trying to translate each word separately every time.

κι is a very common shortened form of και.

Before a vowel, Greek often prefers κι in natural speech and writing:

• κι αν
• κι εγώ
• κι αυτός

So κι αν here is completely normal. You could also see και αν, but κι αν is more idiomatic in this kind of expression.

Because after αν in this kind of clause, Greek uses a subjunctive-type form, not a normal present and not a future with θα.

So:

• αργήσει = the form used here after αν
• θα αργήσει would usually not be used inside this even if clause
• αργεί would sound like a present/habitual statement, not the same structure

In other words, Greek says:

• Έστω κι αν αργήσει = Even if he/she is late / even if he/she arrives late

not:

• Έστω κι αν θα αργήσει

That last version is not the normal grammar here.

Not exactly. It is best understood here as the aorist subjunctive form of αργώ.

For learners, the important point is:

• after αν in clauses like this, Greek uses a verb form that often looks like the form used after να
• αργήσει here does not mean future by itself
• the future-like meaning comes from the whole sentence and context

So the idea is future in meaning, but grammatically this is not simply the ordinary future tense.

Because that is the normal way to form the future in Greek:

• θα
  • verb

Here:

• περιμένουμε = we wait / we are waiting
• θα περιμένουμε = we will wait

So the sentence has:

• a concessive clause: Έστω κι αν αργήσει
• a main future clause: θα περιμένουμε

Very literally, the structure is:

• Even if he/she is late, we will wait.

Greek often leaves out subject pronouns when they are understood from the verb ending.

Here:

• αργήσει = he/she/it is late / arrives late in this context
• περιμένουμε = we will wait

So Greek does not need to say:

• αυτός/αυτή αργήσει
• εμείς θα περιμένουμε

Those pronouns would usually be unnecessary unless the speaker wants emphasis or contrast.

It can naturally cover both ideas depending on context.

Because this is the aorist form, it often gives the sense of a single event or result:

• end up being late
• arrive late

So in many contexts, αργήσει sounds a bit more like arrive late than an ongoing be late. But in English, be late is often the most natural translation.

It is correct and natural, but it sounds a bit more formal, elevated, or literary than some other options.

A very common everyday alternative is:

• Ακόμα κι αν αργήσει, θα περιμένουμε.

That means the same thing: Even if he/she is late, we will wait.

So:

• Έστω κι αν = slightly more formal/stylish
• Ακόμα κι αν = very common and neutral

Yes. Greek word order is fairly flexible.

For example, you could also say:

• Θα περιμένουμε, έστω κι αν αργήσει.

This keeps the same basic meaning, but the emphasis changes slightly:

• first version highlights the condition first
• second version states the main action first

The version you were given is very natural because Greek often places the even if clause at the beginning.

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

So:

• Έστω κι αν αργήσει, = subordinate clause
• θα περιμένουμε. = main clause

This is similar to English:

• Even if he’s late, we’ll wait.

The comma helps show the structure clearly.