Is there a combo ticket for Barcelona sites?
I'm not aware of a good one. A lot of the most popular sights in Barcelona seem to be independently managed, and they seem to sell out every day. I guess they don't need to be part of a city-wide sightseeing scheme that would rake money off the top (just my speculation).
To avoid extremely long ticket lines, you'll need to buy timed tickets in advance for any of these sights you want to see: La Sagrada Familia, Parc Guell, Casa Mila/La Pedrera, Casa Batllo, and the Picasso Museum. The Palau de la Musica Catalana should also be pre-booked since English tours can sell out.
As far as I know, none of those sights requires super-early purchase; you don't need to buy months ahead of time. Just don't be among the folks who show up at the venues without a ticket, hoping to buy one on site. The earliest time slots are the most popular and typically the first to sell out. When you have to pre-schedule multiple sights per day, it's a challenge to figure out the timing. How long will you spend at the first sight? How long will it take to get from Sight 1 to Sight 2? At what point should you plan for a food break, and how long will that take? Scheduling one of the prebooked sights first thing in the morning means that's one timing question avoided.
I have started my research for tickets to Sagrada & Park Güell. The Sagrada site shows timed entry tickets for slots of only 15 minutes with no refunds if you miss the scheduled entry time. Upon arrival, do ticket holders ask those in line for their time slot and then "cut in" to be among those waiting who have tickets for the same 15-minute slot?
It is understood that folks with the next-scheduled entry time move into line in front of those with later times. I went to La Sagrada Familia back in 2016 and don't remember exactly how the line was managed--and the process may have changed. However, there must be a line-minder you can ask if the situation isn't totally clear.
I'm used to 30 minute slots for other venues/museums. Thank you, acraven, for the information.