No tinc cap euro, així que he de pagar amb targeta.

In Catalan, standard negation is formed by putting no before the verb:

• No tinc = I don’t have
• No he de pagar = I don’t have to pay

So no comes before tinc.
You cannot normally put the negative after the verb the way English sometimes does with do not.

Here:

• tinc = I have
• no tinc = I don’t have

Cap is a negative determiner that means something like any or not a single when used with no.

So:

• No tinc cap euro = I don’t have any euros / I don’t have a single euro

This is a very common Catalan pattern:

• No tinc cap problema = I don’t have any problem
• No ve cap amic = No friend is coming / No friends are coming

A useful thing to remember: in standard Catalan, cap usually appears with no in negative sentences.

After cap, Catalan often uses the singular noun, even when English would naturally use a plural.

So:

• cap euro
• cap problema
• cap llibre

This is normal Catalan grammar.
Even though the meaning is plural-like in English (no euros, no books), Catalan commonly keeps the noun in the singular after cap.

Yes, No tinc euros is possible, but No tinc cap euro is stronger and more idiomatic in many contexts.

Compare:

• No tinc euros = I don’t have euros
• No tinc cap euro = I don’t have any euros / I don’t have a single euro

Using cap emphasizes total absence. It often sounds more natural when you mean none at all.

Catalan often drops subject pronouns because the verb ending already shows who the subject is.

• tinc already means I have
• he de already means I have to

So jo is not necessary unless you want emphasis or contrast:

• Jo no tinc cap euro, però tu sí.
  I don’t have any euros, but you do.

In your sentence, leaving out jo is completely normal.

Yes. Així que is a common way to mean so, therefore, or so then.

In your sentence:

• No tinc cap euro, així que he de pagar amb targeta.
• I don’t have any euros, so I have to pay by card.

Other Catalan connectors can express similar ideas, such as:

• per tant = therefore
• per això = that’s why

But així que is very natural in everyday speech.

Good question. Here he de + infinitive is a fixed structure meaning have to + verb.

So:

• he de pagar = I have to pay
• has de venir = you have to come
• hem de marxar = we have to leave

This is different from the perfect tense:

• he pagat = I have paid

So:

• he de pagar = obligation
• he pagat = present perfect

The form he is the same, but the structure around it tells you the meaning.

Both he de pagar and haig de pagar are used.

• he de pagar is standard and very common
• haig de pagar is also common, especially in speech in some areas

For a learner, he de + infinitive is a very safe and standard choice.

You may also hear:

• tinc de pagar in some varieties, though this is less standard in many contexts
• he de pagar remains the best form to learn first

When talking about the method of payment in a general way, Catalan often uses the noun without an article:

• pagar amb targeta = pay by card
• pagar en efectiu = pay in cash

This is similar to English, where we often say by card rather than with a card.

If you add an article, the meaning becomes more specific:

• amb una targeta = with a card (one card, not cash)
• amb la targeta = with the card (a specific card)

So in your sentence, amb targeta is the natural general expression.

Not necessarily. Targeta just means card.

So pagar amb targeta can mean paying by:

• credit card
• debit card
• bank card in general

If you want to be specific, you can say:

• targeta de crèdit = credit card
• targeta de dèbit = debit card

But in everyday situations, amb targeta is often enough.

The comma separates the two parts of the sentence:

1. No tinc cap euro
2. així que he de pagar amb targeta

This is similar to English:

• I don’t have any euros, so I have to pay by card.

The comma helps show the logical pause between the cause and the result. In writing, this is very natural.

Your original sentence is already natural and correct.

A bit more formal:

• No tinc cap euro, per tant he de pagar amb targeta.

A bit more conversational:

• No tinc cap euro, així que haig de pagar amb targeta.

Another very common everyday version:

• No tinc gens d’efectiu, així que he de pagar amb targeta.
  This means I don’t have any cash, so I have to pay by card.

So the original sentence is good neutral everyday Catalan.