Please comment on my 16 day Spain itinerary

2/21 - I would suggest that you take the 10-15 minute walk from Sagrada Familia to the Saint Pau Modernista sight.

Also, consider getting tickets for a performance at the Palace of Catalan Music.

Logistically, it is more convenient to Fly into Madrid and Fly out of Barcelona to go home. I assumed that is what you plan since Barcelona is the last city listed on the tour.

I would tweak the itinerary a bit by adding some places to see along the way.

When you are in Madrid:

2/9 - Visit Toledo

2/10 - El Escorial Palace

When you are in Seville:

2/12 - Day trip to Cordoba

When you are in Granada:

2/15 - Day trip to town of Nerja (beach town) 1 hour bus ride

When you are in Barcelona:

2/22 - Day trip - Girona

You didn't say whether this is your first trip to Spain or even to Europe, so:
1. Be prepared to be flexible. Enjoy the experience even if it means you will have to skip something on your list in order to visit one venue in a memorable, unrushed manner. For example, 2/12 seems a busy day: the Catedral de Sevilla is the 3rd largest church in the world (after St. Peter's in Rome and St. Paul's in London) and can take hours to explore; the Plaza de España is large and has beautiful, unique tiled 'monuments' for many cities and provinces of Spain - fortunately it is open 24 hours (but be especially careful after dark).
2. Do not be late for your appointed ticket times; head to those spots early. Enjoy the exteriors while waiting alertly for your appointment time.
3. Both you and you companion should be well versed on pickpocket and scam prevention. Pickpockets can be anyone: men or women, kids, young adults, older adults, well dressed in business suits, 'backpackers,' other 'tourists' even. Because you are a tourist (expected to be gullible), young (expected to be gullible), and female (expected to be nicer and more willing to help someone in 'need' than a man) you will be prime targets - but you don't have to be victims.
All cities you are going to have pickpockets, and all tourist sites (including museums) have them, but Barcelona is a major center. El Rastro flea market in Madrid is especially busy for them too. I use a money belt / pouch under my clothes (NEVER access in public - hotel room or bathroom stall only!) for my bulk cash, credit card, passport, and info sheet (with reservation & ticket info, etc.) so I can enjoy my vacation without having to be on high alert at all times. This Rick Steve's website has plenty of useful info; click on 'Travel Tips' above.
4. Always be polite: say "Buenos dias" whenever entering any building or to get someone's attention, "Por favor," "Gracias," and then "Adios" when leaving.
5. Stop by the Tourist Information center in Seville for an English language weekly that advertises flamenco; ask the information clerk.
Be prepared so you can enjoy your travels. Have a great time!

I think you've done a good job of researching the options in each city. Although the suggested day-trips may be interesting, I doubt that you'll have time for them on this trip.

You're young and may do a lot better than I do on your arrival day. I am pretty much totally zombified after a sleepless night on the plane. If you arrive in a befuddled state, February 8 will not be a good day to see the Royal Palace. Instead, you could visit the Botanical Garden and perhaps Retiro Park that day. Walking around outdoors is a good way to deal with jetlag.

I think you'll need to buy tickets to Casa Batllo/La Pedrera before you arrive in Barcelona; otherwise, you risk spending a very long time in the ticket line and may not get in at all. I'm not sure about the situation at the Palau de la Musica Catalana. It used to require a tour, which was offered frequently in English, but even in 2016 you couldn't count on walking up to the ticket booth and getting on the very next English tour. Barcelona is a lot busier now than it was even in 2016. Now there is an option for a self-guided tour early in the morning, and I have no idea how heavy the demand is for those early time-slots.

Be prepared for miserable overcrowding at the Picasso Museum. At best it is likely to slow your progress through the museum. At worst, it will send you screaming to the exit. I hope you will be luckier than I was.

I would also be flexible with my plans each day and even where I ate. You have a lot going each day and if someone wanted to sleep late-then sleep late. Ditto for food, it's good that you picked restaurants but if another is recommended or looks good-then change your plans.

Watch out for petitioners in Barcelona that will try to pickpocket you when you are signing their petitions. Also beware of the Rosemary women in Seville by the cathedral. They will try to give you a sprig of rosemary. If you take it, they will then make you buy it and won't take no for answer.

Otherwise, the only other thing I'd recommend more than the Picasso museum is the Miro Museum at Montjuic. We took the cable car up to the top of Montjuic then walked through the park path back down. The Miro Museum is on the way down and gives spectacular views of the city from the rooftop. Also it's a lot less crowded than the Picasso Museum.

2/8 - If you land at 10 am, allow 1-2 hours to clear immigration and collect your bags, and another hour to get to your hotel and drop your bags. Lunchtime! Maybe go to the San Miguel market for drinks and tapas. I would not tour the Royal Palace that day. It sounds like you're landing after a red-eye long-haul flight. Wander outsdoors and stay awake till bedtime. If you can, get tickets in advance to the Royal Palace. Lines can be long even this time of year.

2/9 - The Prado is huge. I hope you have a plan for what you most want to see. If you want to visit 2 art museums on the same day, better to combine the much smaller Reina Sofia and Thyssen.

2/11 - Casa de Flamenco for a very good performance. Don't go to one that offers drinks/food - they are too touristy. The Alcazar is a few meters from the Cathedral.

2/15 - Allow most of the day for the Alhambra - it's huge, lots of walking between the ticketed areas and more to see besides them. Be at the Nasrid entrance at least 15 minutes before your entry time. Large bags and backpacks are not allowed, if you have them, allow time to check them at the nearby building (where there are toilets too and machines for hot drinks). There's not much in the way of food available, you may want to take a picnic lunch with you.

2/22 - there's not much to see on La Rambla (Placa de Catalunya to harborfront). Unless you are staying near the Placa de Catalunya, just take the metro to somewhere closer to the harborfront. I see you already have tickets to the Picasso, so I hope you enjoy it.

2/23 - The MNAC on Montjuic is a stellar art museum and just up the steps from the Magic Fountain. Since you seem to like art, I suggest you go there for the afternoon (allow at least 2 hours). You can pick up tickets for the Palau de la Musica tour on the 22nd. A nice place for lunch is Elsa Y Fred, about 5-7 minute walk. Or go to Orio for pintxos (Basque-style tapas). There's one across the street from the Santa Caterina market - also a 5 minute walk from the Palau.