Έχω μόνο μία χειραποσκευή, γι’ αυτό περπατάω πιο άνετα.

Because χειραποσκευή is a feminine noun.

Greek one changes for gender:

• ένας = masculine
• μία / μια = feminine
• ένα = neuter

So with χειραποσκευή, you use the feminine form: μία.

Yes. Both are used.

• μία is a slightly fuller, more careful spelling/pronunciation.
• μια is very common in everyday Greek.

So both of these are natural:

• Έχω μόνο μία χειραποσκευή.
• Έχω μόνο μια χειραποσκευή.

You will often see μία in teaching materials because it makes the stress clearer.

Because μία already does the job of one / a here.

In Greek, when you use a number like μία, you do not add another article. So:

• μία χειραποσκευή = one carry-on / a carry-on

You would not say something like μία η χειραποσκευή.

It is in the accusative, because it is the direct object of έχω (I have).

• έχω = I have
• what do I have? → μία χειραποσκευή

For this noun, the singular nominative and accusative look the same, so there is no visible ending change:

• nominative: η χειραποσκευή
• accusative: τη(ν) χειραποσκευή

That is why the form may look unchanged even though the function is different.

Χειραποσκευή means carry-on luggage, hand luggage, or carry-on bag.

It is the kind of bag you keep with you instead of checking in.

A useful thing to know: it is a feminine noun:

• η χειραποσκευή
• οι χειραποσκευές

Here γι’ αυτό is the fixed expression meaning:

• so
• therefore
• that’s why
• for that reason

The form γι’ is a shortened version of για before a vowel.

So:

• γι’ αυτό περπατάω πιο άνετα = that’s why I walk more comfortably

This is different from plain για αυτό, which can literally mean for this in other contexts.

So in this sentence, γι’ αυτό is best understood as one expression meaning therefore / so.

Both are correct.

• περπατάω
• περπατώ

They both mean I walk.

This is a very common pattern in Modern Greek: some verbs have two present-tense forms, a longer -άω form and a shorter -ώ form. For example:

• μιλάω / μιλώ
• ρωτάω / ρωτώ
• περπατάω / περπατώ

In everyday speech, περπατάω is very common and sounds natural.

Because here Greek needs an adverb, not an adjective.

• άνετος / άνετη / άνετο = comfortable
  used to describe a person or thing
• άνετα = comfortably
  used to describe how someone does something

Since περπατάω is an action, Greek uses the adverb:

• περπατάω πιο άνετα = I walk more comfortably

So άνετα tells us how the walking happens.

Πιο means more and makes the comparative.

So:

• άνετα = comfortably
• πιο άνετα = more comfortably

This is a very common way to form comparatives in Modern Greek:

• πιο γρήγορα = more quickly
• πιο εύκολα = more easily
• πιο άνετα = more comfortably

Μόνο means only, and here it modifies μία χειραποσκευή.

So the idea is:

• I have only one carry-on

The focus is on the limited amount of luggage.

Greek word order is flexible, but the position of μόνο helps show what is being emphasized. Here it naturally goes before the phrase it affects:

• Έχω μόνο μία χειραποσκευή

You could move things around for emphasis, but this version is the most neutral and natural.

Because Greek often leaves that idea implicit.

Περπατάω πιο άνετα literally means I walk more comfortably, but in context it can naturally imply:

• I can walk more comfortably
• I’m able to walk more comfortably
• I walk more comfortably as a result

Greek often expresses the result directly instead of adding a separate verb like can.

If you wanted to make the idea of ability more explicit, you could say something like:

• γι’ αυτό μπορώ να περπατάω πιο άνετα

But in the original sentence, that would sound a bit heavier than necessary.

Yes, it is very natural.

The sentence has a normal, clear flow:

• Έχω μόνο μία χειραποσκευή, γι’ αυτό περπατάω πιο άνετα.

Literally:

• I have only one carry-on, so I walk more comfortably.

Greek does allow other orders for emphasis, for example:

• Μόνο μία χειραποσκευή έχω, γι’ αυτό περπατάω πιο άνετα.

That puts stronger emphasis on only one carry-on.

But the original version is the most straightforward everyday wording.