There's a lot about your plan that I think is ill advised.
Start by being honest with yourself. You don't have a "10-day itinerary." (Actually, your "itinerary" would work OK for about 14 days, but you don't have that.) You have 8 full days not counting the days you arrive and depart. There's your #1 problem: not enough time. If you want to do all the things on your list, you need to extend your trip. The shortness-of-time issue is made worse by the fact that you're going in December, when days are short, and some things may have limited hours.
Don't plan on much for your arrival day - no matter what time the flight is scheduled (you'll be wiped out from flying across the planet). Same for your departure day - the whole day is consumed by getting to the airport, getting on your flight.
All that aside, I see a number of very red flags in your proposed itinerary...
Fly in to Madrid, move across Spain to Barcelona (it's a large country, even with high speed trains), then return all the way back to Madrid to fly home. Don't do this, it wastes time, money and either burns a full day getting back or puts you at great risk of missing your flight home and requiring a second mortgage.
Never plan to cross a large distance on the day you fly home, to "catch" your flight. The specific answer to your question "to catch 1 pm flight back to LA (is that cutting it too tight?)" is OMG YES THAT'S TOO TIGHT. You need sleep in (or at least near) your departure city your last night. So, you just lost another day (down to 7 usable days now).
You are failing to account for the time it takes to pick yourself up and move to the next destination. For efficient, experienced travelers, between city centers that are well connected, that takes at least half a day, often 3/4 of a day. For you, it's going to consume most of the day. So, when you say "I have X days here and Y days there" you actually have one less day everywhere. So in your proposal, 1 full day in Madrid, 1 full day in Seville, 1 full day in Barcelona...
Honestly, I don't think your plan is realistic or wise, and I think you need to consider some alternative plans. Extend your trip if you can. If you can't, with the time you have, I'd pick 2 (maybe 3) locations. I'd skip Barcelona entirely (are you aware that for some of Barcelona's major attractions, you need to pre-book tickets long in advance?) and stick to Madrid/Seville/Granada. If you must include Barcelona, then just do Madrid (with a day trip to Toledo) and Barcelona, period. Fly in to one, fly home from the other.
Take some time to do a little research about Spain: watch the Rick Steves videos, get the guidebook and read it.
Sorry, I know this is not what you wanted to hear.
Added later: You say you're going "in December" - you mean, December as in next week, or December as in a year from next week? If you're talking around December of this year...good luck. Hopefully you are planning ahead?
