Πιάνω τη βαλίτσα και κατεβαίνω τη σκάλα αργά.

Greek often leaves out subject pronouns because the verb ending already shows who is doing the action.

Here, both πιάνω and κατεβαίνω are 1st person singular, so they already mean I grab / I am grabbing and I go down / I am going down.

You could add εγώ for emphasis:

Εγώ πιάνω τη βαλίτσα...

But in a neutral sentence, Greek usually omits it.

The feminine singular accusative article is basically την, but the final -ν is often dropped before many consonants in normal Modern Greek.

So:

• τη βαλίτσα
• τη σκάλα

are the normal forms here.

The -ν is usually kept before vowels and certain consonant sounds, such as κ, π, τ, ξ, ψ, μπ, ντ, γκ, τσ, τζ.

So a learner should think of τη(ν) as one article with two common surface forms.

Yes, both nouns are in the accusative, but they are not working in exactly the same way.

• τη βαλίτσα is the direct object of πιάνω:
  I grab the suitcase
• τη σκάλα goes with κατεβαίνω in an idiomatic way:
  I go down the stairs / staircase

So βαλίτσα is the thing being grabbed, while σκάλα is the path or route being descended.

Because Greek often uses κατεβαίνω + accusative for the thing you go down along.

So:

• κατεβαίνω τη σκάλα = I go down the stairs
• ανεβαίνω τη σκάλα = I go up the stairs

This is very natural Greek.

English uses a structure with down plus the stairs, but Greek does not need an extra preposition here.

Yes. In Greek, η σκάλα can mean the staircase or the stairs as a single unit.

That is different from English, where stairs is usually plural.

So:

• τη σκάλα = the stairs / the staircase

Greek can also use οι σκάλες in some contexts, but η σκάλα is very common when talking about one staircase.

Πιάνω has a broad range of meanings, including:

• grab
• catch
• take hold of
• sometimes touch or get

In this sentence, it most naturally means something like:

• I grab the suitcase
• I pick up / take hold of the suitcase

A learner might compare it with παίρνω, which often means take in a more general sense.
Πιάνω focuses more on physically taking hold of something.

Both verbs are in the present tense:

• πιάνω
• κατεβαίνω

In Modern Greek, the present can describe:

• something happening now
• something habitual
• a vivid narration of actions

So depending on context, this can feel like:

• I grab the suitcase and go down the stairs slowly
• or I’m grabbing the suitcase and going down the stairs slowly

Greek does not have a separate form exactly like the English am grabbing. Context does that job.

Αργά is an adverb meaning slowly. Greek word order is fairly flexible, and putting the adverb at the end is very natural.

Here it most naturally modifies κατεβαίνω:

Πιάνω τη βαλίτσα και κατεβαίνω τη σκάλα αργά.
= I grab the suitcase and go down the stairs slowly.

You could move it, but the emphasis changes:

• Κατεβαίνω αργά τη σκάλα
• Αργά κατεβαίνω τη σκάλα

The original order sounds smooth and ordinary.

Normally, it describes mainly the second action, κατεβαίνω.

So the sentence is understood as:

• I grab the suitcase
• and I go down the stairs slowly

Not usually:

• I slowly grab the suitcase and slowly go down the stairs

Its position at the end makes it attach most naturally to the second verb phrase.

You can, but it does not mean exactly the same thing.

• κατεβαίνω τη σκάλα = I go down the stairs / staircase
• κατεβαίνω από τη σκάλα = I come down from the stairs / from the ladder

The version with από emphasizes the starting point, and it can sound more like getting down from something.

So for the ordinary meaning go down the stairs, κατεβαίνω τη σκάλα is the better choice.

The written accent marks show which syllable gets the stress:

• Πιάνω → PIA-no
• τη βαλίτσα → va-LI-tsa
• κατεβαίνω → ka-te-VE-no
• τη σκάλα → SKA-la
• αργά → ar-GA

A rough pronunciation of the whole sentence is:

PIA-no ti va-LI-tsa ke ka-te-VE-no ti SKA-la ar-GA

That is not perfect Greek pronunciation, but it helps an English speaker see where the stress falls.