Jennalinda, it's essential to have a ticket or tour that includes the Nasrid Palaces. They are by far the most beautiful part of the Alhambra complex. I'm afraid the tour you purchased doesn't include them. You don't need a tour; the audio guide (at moderate extra cost) is sufficient. You do need a ticket that includes the Nasrid Palaces. There are still full-access tickets available on the official website for the days you'll be in Granada, though that situation could change very quickly. Buy one now. They only cost 19.90 euros.
Here's the homepage to the official ticketing website: https://tickets.alhambra-patronato.es/en/. The "Alhambra General" is the ticket you want, unless you're interested in a number of the additional sights covered by the Dobla de Oro ticket, which is reasonably priced at 27.30 euros. The Dobla de Oro is a good option if the Alhambra General tickets are sold out, but it doesn't save money for most visitors, because they're not in town long enough to see very many sights.
In terms of timing: You are still short on time in Seville, so I'd make a point of heading from Madrid to Seville early in the day on May 6. By comparison, and considering the cities' sizes and things to see, you have more time in Granada, so I'd spend a good part of May 9 in Seville before heading to Granada. You will still have two full days in Granada, which should be adequate. I'm not saying Granada is worth only two days, but Seville needs more than two days. For what it's worth, I think most folks would agree that a third day in Seville is a better use of a first-time visitor's time than a day trip from Madrid to El Escorial.
You should travel from Madrid to Seville by train. There are many trains each day that take about 2-1/2 hours. Flying would obviously take much longer by the time you include traveling to and from the airports and the extra pre-flight time (usually 2 hours) needed at the airport.
All your train tickets except Madrid-Toledo-Madrid will be cheaper if purchased as soon as you get your itinerary nailed down. You can see how fares change by going to the Renfe website and pricing your tickets for your actual travel dates and then for traveling tomorrow. You'll see quite a difference in the cost. You'll also probably see a bunch of Full Train notations for tomorrow. That is not a joke. Spain's about the only country in Europe where individual express trains do sell out. The cheapest tickets ("Basico") are non-changeable and nonrefundable, so be sure your travel dates are firm before purchasing one of those. "Elige" tickets allow changes for 20% of the ticket price and refunds for a 30% fee.