Barcelona trip

Indeed, the ArtCard might be sound in this instance, but normally speaking, tourist cards do not, more so in Barcelona. Most popular sites are not part of these schemes -frankly because they don't need it: why would they want to offer a discount when they're packed almost every day of the year? Besides, if you check the cost of the card (https://bcnshop.barcelonaturisme.com/shopv3/es/product/1/barcelona-card.html) with the actual discounts you're going to get in the sites you are going to visit, you'll see that it really doesn't pay. It rarely does, you'd have to be visiting so many of them, that it's nearly impossible.

Regarding the infamous marketing gimmick about "skippin' the line", you're spot on: buying the ticket online, you're skipping the line in situ to purchase the tickets, but in many sites, there's the other line, the one to get it. Most sites -again, the popular ones- tend to manage flows by setting time slots to get in. When you purchase a ticket, you choose a time slot and can't go in before that time slot (or too long after either). So, let's suppose you're to get in at 11 when you arrive, say at 10:45, you're going to head to the line of the other tourists visiting in the same 11 am time slot. Despite seeming enormous, these lines are relatively fast... everybody should enter at the given time slot.

Having said all that, there are a few (very few, ie Casa Batlló) that offer a marked-up premium ticket by which you can literally waltz in whenever you arrive -no lines. But again, that's subject to not having attained the maximum capacity at that precise instant and, as said, at a heavily marked-up price.

La Mercè has over 600 open-air free to attend simultaneous activities during the 3 days of the festival. The program is released ONLY a few weeks before the festival, and can be browsed at: https://www.barcelona.cat/lamerce/en Keep tuned.

By the way, you surely mean "Gegants" (jah-gants) ;)

Some of the highlights -this was 2023, but most of the activities are the same every year: https://runnerbeantours.com/la-merce-the-main-highlights-of-the-festival/

More info: https://www.barcelona.cat/culturapopular/en/festivals-and-traditions/festes-de-la-merce

Enjoy!

I don't see La Sagrada Familia on that list. The inside of that church is one of the most impressive things I've ever seen. I can't imagine skipping that. You do need to book your timed-entry tickets in advance.

I don’t see the Palau de la Musica on your list. Imo, it’s one of the top Modernista sites.

I also don't see Montserrat on that list. To me, that is a must-see. We were in Barcelona for 2 weeks recently, and Montserrat was a highlight.

I will just give you my impressions of those places you mention that I've visited.
Picasso Museum - I was fortunate to be able to just walk in when there was almost no line for tickets. It was still crowded inside. The rooms are small and the passages narrow. If you are a fan of Picasso, you'll find it interesting. There were a room or two showing his earliest works, and a lot of rooms of his cubist period. It's arranged chronologically with lots of gaps. I would rank it last of the Picasso museums I've been to.
MNAC - I didn't allow nearly enough time (barely 2 hours), so I went back for more on a subsequent trip. If you start at the Miro (which I skipped), it's a pleasant downhill walk to MNAC (there's a little detour through a park with nice views of the city), then walk down to the fountain on the way to the metro.
San Pau - it's a 10 minutes or so walk from La Sagrada Familia, if you do decide to go there. Allow time, San Pau is a large area. BTW the Palau de la Musica, designed by the same architect, is one of the jewels of Barcelona. The English tours sell out, so buy tickets in advance. Be sure to stop at the cafeteria - reasonably priced and almost as beautiful as the theatre.
Santa Catarina market is a good choice, not very touristy and mostly frequented by locals, unlike the Boqueria on La Rambla. Go in the morning or lunchtime. A lot of the market closes in the early afternoon.