1.) Taxis are metered. There's a fare per km depending on the time of the day and the day of the week (weekday vs weekend) and a set of additional charges added (when applicable) to the price in the meter upon arrival to destination. For 2017: http://taxi.amb.cat/documents/956832/1007019/Tarifa+Taxi_2017/23e065d2-2639-4731-a6c4-edbcf7c3df22
2.) There's, however, one instance in which there's a fixed price and that's in the journey airport- port (Moll Adossat*) and vice versa. That's 39€ flat. Note however the city has several ports and marinas and this flat fare is only valid to Moll Adossat, which is where most big cruisers dock, but not all of them, so make sure you know where yours does!
3.) As mentioned, given the overall cost of your vacation taxi fares are probably irrelevant. Having said that, Barcelona taxis are very reasonably priced in comparison to other big cities. As an example, the average cost for a fare airport-city centre (assuming weekday, business hours and normal traffic) is around 30-35€. And a reasonable estimate for a taxi within the city, for most instances, would be under 10€.
4.) Yet depending on where your hotel/apartment is located, there are alternative means to reach the city from the airport, namely bus, metro and train. For example, if near Plaça Catalunya the Aerobus (6€) is a cheaper option; if near Plaça Espanya, both the Aerobus (6€) or regular bus #46 (2.15€, even less with a travel card); if near Casa Batlló, in Passeig de Gràcia, the train (as low as 0.95€ with a T-10 travelcard).... This talking about direct journeys, but you can also transfer at a middle point to reach your destination almost anywhere in the city costing you literally peanuts.