I'm nearly certain Enric has mentioned a bus that goes from very near La Sagrada Familia to Parc Guell. I don't remember the details, but with luck you might find it by Googling. I think the nearest Metro stations to Parc Guell are each about a mile away--quite a long walk, in any case, and uphill as you head to the park, though I believe I recall an outdoor escalator at one or two points, if you approach from the right direction.
In August 2016 most of the Picasso Museum (no one much cared about the ceramics) was nearly as packed as the worst photos I've seen of the Vatican Museums. If you're not much of a fan, I urge you to skip it. Why subject yourself to that, and pay for the privilege? April might be no better, because Barcelona gets heavy tourism year round.
I saw the Picasso Museum as part of the Picasso Tour offered by the tourist office, so I didn't have to obtain my own ticket, but I think it's another of the Barcelona sights for which you must commit to a time when you buy a ticket. Unless you have only one such sight for each day and can schedule each of those first thing in the morning, those timed tickets are flexibility killers. I went to at least four other Barcelona Museums, and the Picasso was the only one at which crowding was a significant issue. I wouldn't be shocked at a 10-minute wait to get inside the Miro and MNAC (though I didn't really wait at all), but once inside, you'd be able to enjoy those museums fully. You won't be doing that at the Picasso, because you have to fight your way through a mog to see the pictures, much less to read the information posted beside them.
