Having in Spain this year for 2 months with a month to go, I can offer these suggestions:
Yes on the Arab baths! Go check out their website. You have to have reservations, but there is a Hamman in Cordoba and Seville. It was a lovely experience. This last time I opted for a longer massage, so a 30 minute massage with the bath. 1 1/2 hours is the amount of time allotted to your visit and is more than enough. You are ready to get out by then.
The train from Madrid stops in ANTEQUERA SANTA ANA, then you get off and get on a bus which takes you to Granada and stops at the train station in Granada. They are building the AVE train to Granada, so until it is finished this is how they do it. You have to pay attention to the stops, it is before the train gets to Malaga. Use the toilet on the train before it stops, they don't have a toilet on the bus (or I didn't see it) and if you are on the evening train, the station is closed so no toilet was available when we arrived. There is no time either between getting off the train and on the bus. It is a very fast transition.
I did the horse show in Cordoba last year and this. Very enjoyable, you can purchase your tickets when you get there. You meniton a day trip to Cordoba??? why not stay overnight? The show doesn't start until late and is 1 hr+ long.
The only way to get to Lisbon from Spain is by bus. From Seville, you go to the Main bus station and take an ALSA bus (alsa.es) it will go to Faro, and maybe farther, I got off in Faro and stayed a few days. From Faro you can take the regional train which runs along the coast only. They have one train station in town - easy to find. I took the train to Portimao, then a taxi to my hotel in Praia de roche. DON"T TRAVEL on the weekend if you can help it! The taxis charge 150% more on Saturday and Sundays in both Spain and Portugal. From Portimao I took the regional train again to Lagos. These train rides were really cheap - under 3 euros. In Lagos I rented a car for a week. Best deal ever. However, I don't think you can do a one way rental. The car was really nice and the price was $160 euros for a week including everything. I was in Lisbon for 2 nights, not long enough, but I had to get back to Lagos. Parking in Lisbon isn't cheap - $15.00 a day. I loved Lisbon. Wish I had more time. I really enjoyed all of Portugal. It is cheaper than in Spain, but it is also windier there. I stayed in a fantastic hotel which I loved, loved, loved!! made all of my hotel arrangements on Booking.com Check out : Casa De Santos, good location, best beds ever, nice staff, beautiful rooms. It was awesome! $48 euros 1 person per night. (April 2015)
On the way back I went from Lagos to Tavira on the train and got off in Tavira. Really nice town. I stayed one night there. Glad I did!
I found travel between cities in Portugal a little harder thus a car makes it way easier. Highly recommend the car in Portugal! Remember to get your International Drivers License before you leave. It is good for one year. Available from AAA.