Getting in at 8 am makes it easy to start in Sevilla. Did you read the Renfe article yet? It will help you immensely in planning for trains. Buy your tickets to Sevilla at the Renfe station in the airport. They'll put you on the next available train you can connect to at Atocha and give you free tickets on the suburban train from the airport to Atocha. The question is what time your flight leaves from Madrid to Miami, to determine whether you really need to spend the last night in Madrid or not.
I would not skip Cordoba - the Mezquita is the second-best sight in Spain and completely unique and the old city center is one of the best-preserved in Spain. Either stay overnight (recommended) or day trip from Sevilla.
There's no benefit to flying from Granada to Madrid. Add the time you need to get to/from the airports and the time you need to check in (and maybe need to check luggage - those short flights generally have low carry-on limits that can be strictly enforced), you won't save more than an hour and it will probably cost you more than a comfortable train ride.
Guides can enhance your experience at any sight, but you can easily appreciate the Alhambra without one. Rent audio guides (you may need to leave photo ID as security - use your driver's license). There are two basic choices - a night visit and a day visit. I recommend doing both! The night visit is to either the Nasrid Palaces or the Generalife. In February I'd go with the Nasrid. It looks completely different at night and you'll also have views of the city below. It does look like they are only available on Friday and Saturday evenings, so that may not work out for you. Then have your daytime visit the next day. Here's how it works. There are several buildings you can only enter with a ticket - the "general" ticket allows access to all of them. The Nasrid Palaces are by timed entry only at 1/2 hour intervals. You can only enter at the time you choose when you buy the ticket. If you are late, you will not be able to enter. So allow enough time to get from the main entrance to the Nasrid. It's about a 20 minute walk, if you don't dawdle. You aren't allowed to bring large bags or backpacks in the Nasrid. There's a building near the entrance where you can check bags for free. That's also one of the few places that have toilets. People start to line up at the entrance as soon as the previous group has entered. Once you're inside there's no limit on how long you can stay, and you can backtrack though there's a one-way route. You can visit the other ticketed parts any time during your visit. The Alhambra "campus" is large. Allow plenty of time, it takes awhile to get from one part to another. It's my understanding that even with an "afternoon" ticket you can enter the grounds when they open in the morning, you just can't enter the ticketed areas before 2 p.m. Conversely, with a morning ticket, you can stay until they close the grounds at 6 p.m. but you can only enter the ticketed areas until 2 p.m.
Buy tickets in advance. You can print them out at any Caixa machine once you're in Spain. You will need the credit card you use to buy them. It's as easy as making an ATM withdrawal, but it does take a few minutes while the machine prints each ticket.