You can find tapas and quick food in a lot of places, but the traditional lunchtime seems to be roughly 2 PM to 4 PM, and the locals will probably not sit down to dinner before 10 PM. Just so you know.
I'm not sure February is (outdoor) picnic weather on Montserrat due to the elevation. Enric will be able to provide guidance on that, and on the risk (if any) of running into weather so bad that even hiking might be problematic. You don't need to pre-book Montserrat, so you can wait for solid weather info before making a final decision. You need to decide before buying your ticket which transportation option you prefer for the final ascent up the mountain. You must take the same one up and down.
I did a tremendous amount of walking in Barcelona just tracking down a lot of modernista buildings, but I gather you're thinking of countryside hiking, and I can't help with that.
Only a limited number of modernista sites are open to the public, and not all of those are by Gaudi, so your options are somewhat limited. I think La Pedrera (Casa Mila) is best, but Palau Guell is a second possibility. Other places are a bit more obscure and/or in more challenging locations.
You've only allowed 90 minutes to see a Gaudi site and get to you lunch location, which is beyond tight; assume that you will start lunch later. I spent 3 hours at La Pedrera, because I was interested in the material about other Gaudi sites on the top floor. Most people do not spend that long, of course. Since your time is limited, I think you should pre-book a ticket for La Pedrera. The wait in line to buy a ticket on the spot can be very long.
For the same reason, you need to pre-book La Sagrada Familia. The usual recommendation is to go for the first time-slot of the day so you have some time in the church before it gets too crowded. If you want to go up one of the towers, that's a separate ticket, which I'd suggest booking for 1 hour later. You can return to the body of the church after ascending a tower if you don't get the two tickets timed perfectly. There's a museum onsite that has interesting information about construction of the church. It doesn't take too long to see but it could be skipped if necessary. Someone here pointed out that once you enter the gift shop, you cannot return to the church, so do be careful about that.
You haven't allowed sufficient time to visit the church and get to the starting point of the planned Gaudi tour.
Parc Guell may need a pre-purchased ticket to avoid a line. Although it's interesting enough, this would not be one of my top targets, and it takes a while to get there if you don't use a taxi. It does have the advantage of variety, since it's outdoors. Still, I'd choose one of the other modernista sites by a different architect, either the Palau de la Musica Catalana or Sant Pau.
The Palau de la Musica Catalana requires a tour (available in English). You might be able to book it when you arrive in Barcelona, but I wouldn't risk just walking up for tickets. The tour is short and the location convenient. Sant Pau is a bit farther out and has multiple buildings (takes more time), and it's partly outdoors. It's much less crowded than the other top modernista sites. There are some English-language tours but my timing was off and I used the audio tour, which was a decent substitute. No pre-booking required.
One other place I'll mention is the Museu Nacional d'Art de Catalunya on Montjuic. It's a large place, and much of the collection does consist of paintings, but it also has an interesting modernsime collection and some wonderful frescoes and architectural elements rescued from very old churches.
