The Tarjeta Dorada discount is 40% Monday-Thursday and 25% Friday-Sunday. Enjoy the extra savings! I'm afraid I don't know about the risk of a sell-out on Saturday. I bought all my train tickets at the station after arriving in Spain. Atocha is a challenging place to buy, to put it charitably. Lines can be very long, and if you go in the evening, you may find they have stopped issuing numbers long before closing time. You can try the ticket machines (change language to English), probably paying with cash because of reported issues with US credit cards. If you have difficulty with that and are short on time, I wouldn't hesitate to use the El Corte Ingles ticket agency in the station, though there will be a service charge of some sort.
When I was in Barcelona a few weeks ago, I asked the tourist-office folks how far ahead I needed to book La Sagrada Familia and Parc Guell in order to get in when they opened. I was told that 2 days ahead would probably be OK for the church and one day ahead for the park. But no guarantees were given. I wasn't booking a tower, though; coordinating the tower with the general entrance to La Sagrada Familia would complicate things a bit. Still, I think if you're not wedded to a specific date and time and have several days in Barcelona, you should be OK. Going early in the day to those two sites does increase the likelihood that they won't be excessively crowded.
The tourist office sells tickets to many of the places you list, but not tower entry for La Sagrada Familia. If you're going to stop by there early in your visit anyway, you can buy a lot of your tickets in person if you're ready. There's a 2-euro-per-ticket service charge. It was worth it to me for the convenience of getting the tickets there.
A friend booked our 5 PM English-language tour of the Palau de la Musica Catalana several weeks ahead, but I assume that much advance notice isn't necessary. You don't want to miss it, though. I'm not sure the tourist office sells tickets to this site.
The Casa Battlo folks seem determined to get as many people into that building as they can. There can be a line, but that's not the only problem. Even if you buy tickets in advance, conditions inside are likely to be very crowded. La Pedrera is also very popular but wasn't quite as mobbed when I was there. At the end of your visit you'll find lots of information about Gaudi's other buildings, including those located in other cities. If you choose to, you could probably spend 2-1/2 hours at La Pedrera.
For a beautiful mondernista site that gets very few tourists, try Sant Pau. This is a multi-building site, so you want decent weather. Self-guided tours cost only 10 euros, a real bargain compared to a lot of other places in Barcelona. Allow plenty of time to see the upper floor of the main building, which comes at the end of the visit. Don't go late in the afternoon!