What dates will you be in Barcelona?
I think you'll find the two other major Gaudi sights (Casa Mila/La Pedrera and Casa Batllo) are open seven days a week. I suppose there might be an exception around Easter, but likely not. Churches are likely to be open as well.
I've been to the Sant Pau modernista site twice--August 2016 and May 2019--and saw no sign of any sort of ticket line. I don't know whether there's a COVID-related requirement to get tickets in advance, but if so, I cannot imagine there is any need to get that ticket more than one day ahead of time. I'd wait on that one, at least until it's almost time to leave on your trip. Why commit any more money in advance than you have to?
The three sites you mentioned are all rather time-consuming. Sant Pau has multiple buildings set on attractive grounds; La Sagrada Familia has a lot to see inside and outside the church, and the museum has a good explanation of Gaudi's techniques; Parc Guell has both the area you'll be paying to enter and a large free zone you might also like to see. I wouldn't want to commit to doing all of those on the same day. I'd pick La Sagrada Familia as the first stop, because I think you'll benefit more there from being in the first group to enter.
Since Parc Guell is outdoors, I'd prefer to have an idea of the weather forecast before I bought that ticket. I'd probably monitor the website to be sure ticket availability is OK and then buy much closer to the time of my visit, ideally with access to a reasonably reliable weather forecast. You do have to get the ticket ahead of time; they no longer sell tickets at the park.
We probably need for one of our Barcelona folks to address your question about special happenings on Sunday. All I know of is the sarzana dances. I remember seeing outdoor antique stalls near the Cathedral but don't remember what day of the week that is.