As far as I know, there is nothing about a day-trip to Montserrat that has to be pre-booked. I would wait and make a day-of-travel decision, because you may desperately need that day in Barcelona, or you may be unlucky with the weather.
When the time comes, just go to the rail station under the Placa d'Espanya and buy the combo round-trip ticket from a machine. When I was there in 2016 (headed elsewhere), there was a Renfe (?) staffer hanging around the machines, assisting tourists. You need to decide before making the purchase which mode of transportation you want to use for the second part of the trip (should be explained in your guidebook). And I believe Enric has recommended here not opting for the combo ticket that includes a meal.
The Dali Theatre and Museum ticket should be booked in advance. That place gets a lot of bus tours, and it's quite possible for certain time-blocks to fill up. Since you'd be traveling out of town for this, you wouldn't be happy to be told you could buy a ticket but had to return in 2 or 3 hours. If you have the option, I'd opt for a weekday. The T&M is accessible from France, and I'm guessing a lot of the French traffic arrives on weekends.
Another reason to book the Dali site in advance is that there may still be some inexpensive (non-refunfable/non-changeable) train tickets left to Figueres. They will be rather expensive at full fare. Renfe.com is a problem for many foreign tourists. I'd try buying the rail tickets from loco2.com or trainline.com. At this moment loco2 should be a bit cheaper; it will start charging fees later this year.
As for the Alcazar in Seville, part of my trip to that city fell during Holy Week this year, which is a very busy time. Lines for both the Alcazar and the Cathedral were very long, outdoors and uncovered. I bought the Alcazar ticket online, I think just one day in advance. However, I had a long stay in Seville and didn't need to be picky about my entry time. On a short trip you will benefit from putting that time-specific sight first thing in the morning, and demand for those tickets may cause them to sell out earlier.
Tickets for the private apartments in the Alcazar sell out far in advance (at least weeks, I believe). I have not read that the apartments are all that special; I think the ticket situation is due to a severe limit on the number sold. The Alcazar itself is large and can accommodate a lot of visitors; you just don't want to stand in that long ticket line