* In almost all cases the different cards (there are a few) will end up costing more than you spend.

Of course, the only way to determine this is to make a list of what you want to do, look at what the card offers for those places and calculate the benefits.

Be aware that many times the sites of those cards present a misleading comparison and the "regular" price they show is usually higher than the actual one.

Checks I've made showed that the Barcelona Card is the only card that in some combinations might be worthwhile, but with a small margin, if you're focus is museums. Their publications are more accurate but there are still a few incorrect presentation (like with the MUHBA where they show each site as 7€ where in reality if you but the 7€ ticket it includes most of those sites). You should also remember that most of the times the free option is for the basic entry, without extras like temporary exhibitions or special areas for extra cost.

As for the travel card, most do not use transit that much as the city is pretty compact, very walkable and most sites are within a relatively small radius (of ~3.2 km/2 mi from the center/Pl. Catalunya) and many are within a short walking distance from each other so it's easy to plan each day around a small walkable area.

Apart from that, be aware that the transit card attached to the Barcelona Card is the touristic car HolaBCN which does include most integrated transit means but not all of them (it does not include night buses, for example). If you want an unlimited card the best option right now is the T-usual, which is an unlimited fully integrated card for 30 days and untill the end of the year it is sold with a 50% discount for 21.35 €.

* Unfortunately for you there is no Camp Nou tour right now as it is going through a major renovations. the team plays now in the Estadi Olímpic Lluís Companys on Montjuïc. The last date for their return to Camp Nou is November 2024, but this is not final and even than work will continue so i doubt they'll reinstate the tour. There is a temporary museum with a virtual tour near Camp Nou.

* I've never considered a "best time" to visit Sagrada Familia. Each time it's a bit different but IMO, unless you're looking for a specific light situation for a professional photo or for Instagram I don't think it should be an issue so I suggest you decide by the plans you have for the day. after Casa Milà it´s fine as it´s not too far on foot. you can also do Park Güell in the morning than walk down hill through Vila de Gracià (leave time to walk around and go into shops and a bar/restaurant /coffee shop) to Sagrada Familia.

* The day is also not as important. of course weekends are busier so a weekday will be a bit better but all those places have a maximum capacity so it won't be flooded.

* National Day of Catalonia is a holiday here but attractions are open on holidays (with the exception of Christmas day and New Year's day when almost all are closed). Just make sure to prebook and check opening hours as some places, usually museum (but not all) will close early on Sundays and holidays (usually at around 15:00/3pm).

As for shops, this day is one of the days that shops can be open (between 12:00/12pm - 20:00/8pm) in the touristic area (which is basically a huge area of the city center). This does not mean that all shops will open. Usually small neighborhood shops do not open and most supermarket chains tend to remain closed even on allowed days but shopping centers/streets and bigger chain stores will be open. Supermarkets like Aldi, Lidl and Carrefour also tend to open as well as El Corte Inglés department store, which also has a supermarket (but an expensive one). There are also countless of small grocery/convenient stores that are open year-round, some even 24h. Restaurants/Bars.Coffee shops will usually be open (some tend to remain closed on Mondays) but some might be closed, at least for part pf the day.

For specific places always check opening hours.

* public transport works every day, all day (during the night there are night buses and the metro that closes at 02:00/2am on Fridays and eve of holidays and runs nonstop between on nights between Saturdays and Sundays). Frequency will be lower. with buses it depends on the line but in most cases it's between 10-20 minutes. The metro has higher frequencies. It won't be a problem.