Spending money in cruise ports?

My husband and I are going on a cruise in Oct on Carnival. We will be stopping at Catalina Island and Ensenada Mex. While we are there how does spending money work for food,gifts,activities? Do either of them take credit/debit cards? Or should we only use cash and only have small bills $20 or less? Is it safe to use your debit/credit card in Mex? While in Ensenada do they accept our money or do we have to get pesos or what ever? Also while in Ensenada if they do take our cash or cards will it be calculated in our money or do they do the exchange rate? I hope you understand what I want to know. Sorry for the stupid questions just this is our first time and I am a little confused and I just want to be prepared!! :~) Thank You all so much