Αν τσαλακώσεις το πουκάμισο, θα πρέπει να το σιδερώσεις ξανά.

Because Greek is treating both actions as single, complete events.

• τσαλακώσεις = you wrinkle / you crumple (one completed action)
• σιδερώσεις = you iron (one completed action)

These are aorist subjunctive forms, which are very common:

• after αν for conditions
• after να
• after θα πρέπει να

So:

• Αν τσαλακώνεις το πουκάμισο... would sound more like a repeated or ongoing action: if you keep wrinkling the shirt / if you wrinkle shirts in general
• Αν τσαλακώσεις το πουκάμισο... means if you wrinkle the shirt in a particular case

That matches the English idea very well.

No. They may look future-like to an English speaker, but they are not future tense by themselves.

They are subjunctive forms, and in this sentence they appear because of:

• αν → Αν τσαλακώσεις...
• να → θα πρέπει να το σιδερώσεις

In Greek, the future is usually marked by θα, not by the verb ending alone.

So:

• τσαλακώσεις on its own is not you will wrinkle
• θα τσαλακώσεις would be you will wrinkle

Likewise:

• σιδερώσεις = subjunctive form
• θα σιδερώσεις = future tense

Both are possible, but they mean slightly different things.

• πρέπει να το σιδερώσεις = you have to iron it
• θα πρέπει να το σιδερώσεις = you will have to iron it

In this sentence, the speaker is talking about the result in the future of wrinkling the shirt. So θα πρέπει να fits naturally:

• If you wrinkle the shirt, you will have to iron it again.

So θα is making the obligation point to what will happen next.

The two το words are doing different jobs.

1. το πουκάμισο

   • here το is the definite article
   • it means the
   • so: the shirt

2. να το σιδερώσεις

   • here το is a direct object pronoun
   • it means it
   • it refers back to the shirt

So the sentence is structured like:

• If you wrinkle the shirt, you will have to iron it again.

This is completely normal Greek.

Because Greek usually does not need subject pronouns when the verb ending already shows the subject.

Here:

• τσαλακώσεις = you wrinkle
• σιδερώσεις = you iron

The ending -εις tells you the subject is you singular.

So Greek often leaves out εσύ unless it wants to add emphasis or contrast.

For example:

• Αν εσύ τσαλακώσεις το πουκάμισο...
  would sound more emphatic, like if you wrinkle the shirt...

But in a normal sentence, Greek just omits it.

ξανά means again.

So:

• να το σιδερώσεις ξανά = to iron it again

Putting ξανά at the end is very natural. Greek word order is fairly flexible, but this position is common and clear.

You may also hear forms with ξανα- attached to the verb in everyday speech:

• να το ξανασιδερώσεις

This also means to iron it again.

Both are correct.
Very roughly:

• να το σιδερώσεις ξανά = slightly more neutral/separate
• να το ξανασιδερώσεις = very common in everyday speech

Yes, in this sentence it matches wrinkle very well.

τσαλακώνω can mean:

• wrinkle
• crease
• crumple

It is often used for clothes, paper, fabric, and similar things.

Examples:

• Τσαλάκωσες το πουκάμισο. = You wrinkled the shirt.
• Το χαρτί τσαλακώθηκε. = The paper got crumpled.

So in clothing contexts, wrinkle or crease is a very natural translation.

You could, but it changes the feel.

• Αν τσαλακώσεις το πουκάμισο...
  = if you wrinkle the shirt
  one specific event

• Αν τσαλακώνεις το πουκάμισο...
  = more like if you are wrinkling the shirt or if you tend to wrinkle the shirt depending on context

So the original sentence uses τσαλακώσεις because it is talking about a single possible action and its consequence.

That is the most natural choice here.

Yes, in many everyday situations.

• αν = standard if
• άμα = also means if / when, often more conversational

So you could hear:

• Άμα τσαλακώσεις το πουκάμισο, θα πρέπει να το σιδερώσεις ξανά.

This is natural spoken Greek.
The original with αν is a little more neutral and standard.

You may also see εάν, which is a more formal version of αν.

A rough pronunciation guide:

• Αν → an
• τσαλακώσεις → tsa-la-KO-sees
• το πουκάμισο → to poo-KA-mee-so
• θα πρέπει → tha pre-PEE
• να το σιδερώσεις → na to see-the-RO-sees
• ξανά → ksee-NA

A few useful notes:

• τσ sounds like ts in cats
• που sounds like poo
• δ in modern Greek sounds like the th in this
• The written accent mark shows the stressed syllable:
  • τσαλακώσεις
  • πουκάμισο
  • πρεπέι? No — stress is πρέπει = PRE-pi? Actually in standard pronunciation it is PRE-pi? Wait, spelling stress is on πρέ-. So pronounce it PRE-pee
  • σιδερώσεις
  • ξανά

The most important thing is to keep the stress in the right place.

It follows a very common Greek conditional pattern:

• Αν + subjunctive, θα + verb / expression

Here that becomes:

• Αν τσαλακώσεις το πουκάμισο, θα πρέπει να το σιδερώσεις ξανά.

You can think of it as:

• If X happens, Y will follow.

More literally:

• If you wrinkle the shirt, you will have to iron it again.

This is a very useful pattern to learn, because you can build many sentences with it:

• Αν αργήσεις, θα χάσεις το λεωφορείο.
  If you are late, you will miss the bus.

• Αν το ξεχάσεις, θα έχεις πρόβλημα.
  If you forget it, you will have a problem.

So this sentence is a good model for a common Greek structure.