“¿Puedo pagar con tarjeta?” means “can I pay with a credit or debit card?”. You do not need to be specific.
If a salesperson asks you for a “NIP” when you are paying, it means you need to enter your “PIN” number. This will only happen with debit cards.
Credit cards are widely used in Latin America. American Express is an exception to the rule as many places do not take those. Visa and Mastercard are taken almost everywhere. Every department store will take them. The only place you may not be able to use them are for small corner shops or in markets (and even there you may be surprised).
Malls and department stores are ubiquitous in most cities in Latin America. People coming from the US, Canada or Europe will find they are almost identical to what they are used to.
“Para usted” means “for you”. In some parts of Latin America they may be more informal and say “Para ti”.
“Pague en la caja” means “please pay at the cashier”.