Δεν θέλω να σου χρωστάω λεφτά για πολύ, γι’ αυτό πέρασα από την τράπεζα πριν έρθω.

Greek does not use an infinitive the way English does. So after θέλω you normally get να plus a finite verb.

• θέλω να φύγω = I want to leave
• θέλω να κοιμηθώ = I want to sleep

So Δεν θέλω να σου χρωστάω is literally something like I don’t want that I be owing you, but in natural English it is just I don’t want to owe you.

χρωστάω here is the imperfective form, which fits the idea of an ongoing state: to be owing or to be in debt.

The speaker means: I don’t want to keep owing you money for long.

If you used a perfective form such as χρωστήσω, it would sound more like to come to owe or to owe as a single completed event, which is not the point here. The sentence is about a continuing situation, so χρωστάω is the natural choice.

σου means to you.

It is the weak form of the pronoun, often called a clitic, and in Greek these short object pronouns usually come before the verb:

• σου χρωστάω = I owe you
• σου λέω = I tell you
• σου δίνω = I give you

So να σου χρωστάω λεφτά = to owe you money.

λεφτά is the normal everyday Greek word for money, and it is grammatically plural.

So even though English uses the singular mass noun money, Greek commonly uses λεφτά:

• Δεν έχω λεφτά = I don’t have money / I have no money

A more formal or neutral word is χρήματα, which is also often plural in use. λεφτά is very common in speech.

Here για πολύ means for long or for very long.

It is short for the fuller idea για πολύ καιρό = for a long time.

So:

• Δεν θέλω να σου χρωστάω λεφτά για πολύ
  = I don’t want to owe you money for long.

Greek often leaves out καιρό when it is obvious.

Yes. γι’ αυτό is a contracted form of για αυτό.

In this expression it means that’s why, for that reason, or so:

• για αυτό / γι’ αυτό = for that / that’s why

The apostrophe shows that a vowel has been dropped in pronunciation/spelling. In everyday writing, γι’ αυτό is very common.

Yes, the basic meaning of περνάω is pass, but in many contexts περνάω από... means stop by, go by, or drop in at a place.

So πέρασα από την τράπεζα means:

• I stopped by the bank
• I went by the bank

In this sentence, the idea is clearly that the speaker went to the bank in order to deal with the money situation.

Also, πέρασα is the aorist, so it presents the action as a single completed event: I stopped by.

Literally, από often means from, but with verbs like περνάω it can mean by, via, or past.

So:

• περνάω από το σπίτι σου = I stop by your house
• πέρασα από την τράπεζα = I stopped by the bank

This is a very common pattern in Greek. You should learn περνάω από + place as a chunk meaning go by / stop by a place.

After πριν meaning before, Modern Greek usually uses the subjunctive-type verb form without να.

So:

• πριν έρθω = before I come / before I came
• πριν φύγεις = before you leave
• πριν πάμε = before we go

This is normal Greek. A learner may expect να, because έρθω is a subjunctive form, but after πριν the να is usually omitted.

έρθω is the perfective non-past form of έρχομαι. After πριν, Greek often uses this form to refer to an action viewed as a whole.

So πριν έρθω literally looks like before I come, but depending on context it is often translated into natural English as before I came or before coming.

In this sentence:

• πέρασα από την τράπεζα πριν έρθω
  = I stopped by the bank before I came

Greek is not using an English-style past tense here. It is using the form that Greek normally wants after πριν.

Greek often leaves subject pronouns out because the verb ending already shows the person.

• θέλω = I want
• πέρασα = I stopped by / I went by
• έρθω = I come

So there is no need to say εγώ unless you want emphasis or contrast.

For example:

• Εγώ δεν θέλω να σου χρωστάω λεφτά
  would sound more like I don’t want to owe you money, with extra emphasis on I.

Yes, they are the same verb.

• χρωστάω is very common in everyday speech
• χρωστώ is a shorter form, often a bit more formal or stylistically different

Both mean I owe.

So you may see:

• Σου χρωστάω λεφτά
• Σου χρωστώ λεφτά

Both are correct. In casual spoken Greek, χρωστάω is extremely common.

Usually, in context, yes. Even though πέρασα από literally sounds like I passed by, it often means I stopped at or I dropped in at a place.

With τράπεζα, and especially after saying they did not want to owe money, the natural interpretation is:

• they went to the bank
• probably to get money or handle the payment

So this is one of those cases where the idiomatic meaning matters more than the literal word-for-word meaning.