Αν η πληρωμή αργήσει, ο λογιστής θα στείλει ξανά το τιμολόγιο με email.

In Greek, you normally do not use θα after αν.

After αν, Greek uses a subjunctive-type verb form, often called the perfective non-past in modern grammar. So αργήσει is exactly the kind of form you expect here.

That means:

Αν η πληρωμή αργήσει = If the payment is late / if the payment gets delayed

This is similar to English, which also usually avoids will in an if clause:

If the payment is late, ...

not usually

If the payment will be late, ...

Αργήσει comes from the verb αργώ.

Here, αργήσει is the perfective non-past form. In many learner materials, you may also see it described as an aorist subjunctive form after words like αν, να, and θα.

Why this form? Because the sentence is talking about one possible event in the future: the payment might be delayed. Greek often uses the perfective form for a single whole event like that.

Compare:

αργεί = is late / is being late / tends to be late
αργήσει = be late once / get delayed

So in this sentence, αργήσει fits better than αργεί.

No. στείλει by itself is not past tense here.

With θα, it makes a future meaning:

θα στείλει = will send

Just like αργήσει, στείλει is the perfective non-past form. After θα, that form usually gives a simple future meaning.

Compare:

στέλνει = sends / is sending
θα στείλει = will send
έστειλε = sent

So the past form is έστειλε, not στείλει.

Greek uses the definite article much more often than English.

In this sentence, all three nouns are presented as specific things already known from the context:

η πληρωμή = the payment
ο λογιστής = the accountant
το τιμολόγιο = the invoice

Even where English might sometimes sound more natural without an article in a business context, Greek often keeps it. So this sentence sounds very normal and natural with all three articles.

Here is the basic breakdown:

η πληρωμή is nominative because it is the subject of αργήσει.

ο λογιστής is nominative because it is the subject of θα στείλει.

το τιμολόγιο is the direct object of θα στείλει, so it is accusative. Because τιμολόγιο is a neuter noun, its nominative and accusative singular look the same: το τιμολόγιο.

So even though English relies heavily on word order, Greek also shows grammatical roles through articles and endings.

Yes, it could.

ξανά means again, and Greek adverbs are fairly flexible in position. In the sentence

ο λογιστής θα στείλει ξανά το τιμολόγιο

ξανά modifies the action send again.

A very common alternative is:

ο λογιστής θα ξαναστείλει το τιμολόγιο

Here ξανά is effectively attached to the verb as ξανα-. This is extremely common in everyday Greek.

So both are natural:

θα στείλει ξανά το τιμολόγιο
θα ξαναστείλει το τιμολόγιο

The second one often sounds a bit more compact and conversational.

Because here με email means by email, so it expresses the method or means.

In Greek, when you describe the way something is done, you often do not need an article:

με email = by email
με λεωφορείο = by bus
με το χέρι can also happen, but that has a different pattern because it is a regular noun phrase

If you said με ένα email, that would sound more like with one email or in a single email, which is a more literal, countable idea.

You may also hear:

μέσω email

That is also correct and sounds a bit more formal or administrative.

Not completely. Greek word order is more flexible than English word order.

The given sentence is neutral and very natural:

Αν η πληρωμή αργήσει, ο λογιστής θα στείλει ξανά το τιμολόγιο με email.

But Greek can move things around for emphasis. For example, other arrangements are possible, although they may sound less neutral or put focus on a different part of the sentence.

The reason this flexibility is possible is that Greek marks grammatical relationships with articles and endings, not just word order.

Still, for a learner, the given order is a very good model: if-clause + subject + future verb + object + method

Yes, definitely.

You could say:

Αν η πληρωμή καθυστερήσει, ο λογιστής θα στείλει ξανά το τιμολόγιο με email.

That is also very natural.

The difference is mainly nuance:

αργήσει suggests be late
καθυστερήσει suggests be delayed

In business or formal contexts, καθυστερήσει may sound slightly more explicit or formal, but αργήσει is also perfectly normal.

Yes.

εάν and αν both mean if.

In this sentence, the difference is mostly one of style:

αν = the usual everyday form
εάν = slightly more formal or careful

So both are correct:

Αν η πληρωμή αργήσει, ...
Εάν η πληρωμή αργήσει, ...

Because the sentence begins with a conditional clause:

Αν η πληρωμή αργήσει

and then moves to the main clause:

ο λογιστής θα στείλει ξανά το τιμολόγιο με email

Greek commonly separates that opening if clause from the main clause with a comma, just like English often does.

So the punctuation here is very standard and helps the sentence read clearly.