Lodging - In Barcelona I stayed at Pensio2000. It was cheaper than anything else I found in Barcelona and was fine. It's "different." I would definitely stay there again. I think it must have been a large private apartment (3rd floor walk-up) that was remodeled. There are about 6 rooms of various sizes, all with private bathrooms. It's run by a middle-aged couple who are very friendly and helpful. If you want more information PM me. The location was excellent, a 5-10 minute walk to the Barri Gotic, Ramblas, markets and literally across the street from the Palau de la Musica (a must-see). The street itself was very quiet at night. I traveled solo in Barcelona and Andalusia and was never anywhere that felt unsafe.
Sights - In Barcelona, I had a list of museums (I love museums), but the weather was beautiful (February) and so was the city, so I didn't visit any! I'm not a big fan of Gaudi, so the only building I toured was La Sagrada Familia. Montaner is much more "up my alley" and I went to his buildings: Sant Pau Recinte Modernista, Casa Lleo i Morera, and the Palau de la Musica, loved them all. The Font Magica (Magic Fountain) in the evening for the sound and light display. I took one TI morning walking tour and it was very good. Their website gives a lot of information. Consider a 1/2 day trip to Monserrat or a day trip to Girona, easy to do on your own by train. One of the best things I did was a guitar concert for €19 (with 4 artists - excellent music and entertaining show).
Sights - In Seville, the top sights are the Alcazar and the Cathedral. For me the best part of the cathedral was climbing the tower for the view. The show at La Casa del Flamenco was quite good and less touristy (and less expensive - €15) than some of the others. Be wary of recommendations from tour guides and hotels that offer to make the reservation for you, they may be getting a kickback. Visit the bullring and its museum (chances are there won't be any bull fights while you are there). The absolute, hands-down best sight is a day trip by train to Cordoba to visit the Mezquita. Since the train to Barcelona goes through Cordoba, you could also stop for the day on your way back from Seville, storing your bags at the station (maybe the bus station across the street from the train station). You would buy separate tickets for each leg of the journey. The Mezquita is best first thing in the morning if you can pry yourselves out of bed for an early train ride.
Food - Dinner in Spain generally doesn't start before 9 or 10 p.m. You can get big lunches from about noon-2 p.m. and tapas any time. In Seville, the best tapas (I rely on the word of a knowledgeable local) are at Bodeguita Casablanca (calle Adolfo Rodriguez Jurado 12) very near the Alcazar and the cathedral. I also had good tapas at Bar Las Teresas. In Barcelona, you can graze for lunch or dinner (or buy for a picnic) at the markets. There's the huge Boqueria which attracts the tourists and the big Mercat de Santa Caterina, that is not far away and is frequented more by locals . . . and somewhat cheaper.
I don't really see any option to splitting your time in Barcelona. Trains in Spain are great. Plan to be at the station about 15 minutes before the train leaves, so you have time to find the platform and pass your bags through security. You will get huge discounts by buying tickets in advance, usually 3 months out, but it varies. The best website for using the trains and navigating the website is here. It's long, but it will tell you everything you need to know.