Nawet jeśli jestem zmęczona, wreszcie piszę odpowiedź na ważny mail.

Nawet jeśli means even if.

It introduces a kind of condition: even if I am tired.
By contrast, chociaż and mimo że usually mean although / even though, so they more strongly suggest that the thing is a fact.

So:

• Nawet jeśli jestem zmęczona... = Even if I’m tired...
• Chociaż jestem zmęczona... = Although I’m tired...

In real-life speech, people sometimes use them in similar situations, but the basic distinction is:

• nawet jeśli = conditional / regardless
• chociaż, mimo że = concession / known fact

Because the adjective agrees with the speaker’s gender.

• A woman says jestem zmęczona = I am tired
• A man says jestem zmęczony = I am tired

In Polish, some forms that refer to the speaker still show gender, even in the first person singular.

It can mean both.

Polish does not usually make a separate grammatical distinction like English does between:

• I write
• I am writing

So piszę can mean either one, depending on context.

In this sentence, because of wreszcie and the situation described, the most natural English translation is I am finally writing.

Because piszę is imperfective, and it focuses on the action as a process.

• piszę = I am writing / I write
• napiszę = I will write / I will finish writing

So:

• piszę odpowiedź focuses on the act of writing the reply
• napiszę odpowiedź focuses more on completing it

In this sentence, the speaker is describing the ongoing action, so piszę fits better.

Wreszcie means finally or at last.

It often suggests delay, relief, or that something took a long time to happen.

Yes, w końcu is also possible in many contexts:

• wreszcie = finally, at last
• w końcu = finally, eventually, in the end

Often they are close in meaning, but wreszcie can sound a little more like relief: finally!

Because nawet jeśli jestem zmęczona is a subordinate clause, and in Polish subordinate clauses are normally separated by a comma.

So the structure is:

• Nawet jeśli jestem zmęczona, = subordinate clause
• wreszcie piszę odpowiedź na ważny mail. = main clause

This comma is standard Polish punctuation.

Here odpowiedź is the direct object of piszę, so it is in the accusative.

The important thing is that this noun does not visibly change in the accusative singular.

• nominative: odpowiedź
• accusative: odpowiedź

That is normal for many feminine nouns ending in a soft consonant, like -ść, -ź, -ń, etc.

So even though the case changes grammatically, the form stays the same.

Because odpowiedź normally connects with na + accusative when it means reply/answer to something.

For example:

• odpowiedź na pytanie = an answer to a question
• odpowiedź na mail = a reply to an email

So na is simply the standard preposition used with this noun.

The related verb works similarly:

• odpowiadać na pytanie
• odpowiadać na mail

Because mail is a masculine inanimate noun, and after na here it is in the accusative.

For masculine inanimate nouns, the accusative singular is usually the same as the nominative singular. So:

• nominative: ważny mail
• accusative: na ważny mail

That is why the form stays ważny mail.

Yes, in everyday Polish, maila is very common.

You may hear:

• mam maila
• czekam na maila
• odpisałem na maila

This is very common colloquial usage.
The version in your sentence, na ważny mail, is perfectly understandable and looks more neutral or standard.

So as a learner, it is good to recognize both:

• mail = neutral/standard-looking form
• maila = very common in spoken Polish

Mail is very common in modern Polish, especially in everyday speech.

You can also see:

• e-mail
• email
• wiadomość e-mail

All are understood. Very roughly:

• mail = casual, common
• e-mail / email = a bit more formal or careful

So the sentence sounds natural.

Yes. Polish word order is fairly flexible.

This version:

Nawet jeśli jestem zmęczona, wreszcie piszę odpowiedź na ważny mail.

puts emphasis first on the concessive idea: even if I’m tired.

You could also say something like:

Wreszcie piszę odpowiedź na ważny mail, nawet jeśli jestem zmęczona.

That still makes sense, but the focus changes. The original sentence sounds natural if you want to foreground the tiredness and then contrast it with the fact that the speaker is finally writing.

So in Polish, changing word order often changes emphasis more than basic meaning.