I don't dare give you aggregate time estimates because 1) I'm a very fast walker and 2) I had a nice, long stay in Barcelona and didn't pay attention to how much time I spent doing most things.
You can use Google Maps to estimate your walking time between key points. It will also estimate public-transportation times, but I wouldn't necessarily trust those.
For La Sagrada Familia without a tower ascent, I think 90 minutes would be adequate for a large percentage of visitors, and most would probably spend a bit less time. 90 minutes would give you some time in both the museum and the shop. If you're going to take a lot of pictures or buy all your holiday gifts in the shop, you'll need extra time.
Allowing an hour for lunch may be inadequate if you're expecting a sit-down meal rather than a sandwich or a salad in a café-style place. I can only suggest that you pad your schedule a lot. Use the extra time to walk around the Eixample, looking at the exteriors of the many interesting buildings.
At Parc Guell it will matter a great deal whether you want to line up to go inside the gatekeeper's cottage. (I did not.) I think the line was already 45 minutes long by the time I noticed it. The park is quite large. I stayed in the Monumental Zone (the part you pay for), but that's only a part of the park. I think an hour inside the park would be about the rock-bottom minimum; otherwise, why traipse all the way out there? You could certainly spend a great deal more time than that.
I think I spent at least 2 hours in the Picasso Museum. That included no time waiting in line because I took the Tourist Office's Picasso tour. Crowding will almost certainly be a factor. It will slow your progress through the museum because you'll have to wait to get close enough to see some of the paintings. Of course, it might be so crowded that you give up quickly.
Someone suggested using a smartphone (or tablet with Wi-Fi) in the morning to book entry to Barcelona sights for later in the day when ones schedule is a bit clearer. That might work for Casa Mila (I am not guaranteeing it), but I think trying to handle the Picasso Museum that way would be risky. Another possibility is to check the official websites to see whether the places you want to visit have extra-cost wildcard tickets that don't tie you to a specific entry time. (I don't know whether they're day-specific.) I know that some Barcelona sights make such tickets available. That would allow you the flexibility you're seeking without any chance of a sell-out.