Congratulations on your retirement.
I suppose why nobody has answered until now is that you've ask quite a few questions. I'll try to help with two.
As for visiting Cadiz, I've been back to Spain 4 times and I feel that any Spanish city is worth the visit. I've even explored some out of the mainstream ones like Badajoz. I don't think you can go wrong visiting any Spanish town.
As for inexpensive places to stay, in the time frame beginning the latter part of August, I wouldn't be too worried about not having reservations. My advice is when you arrive at a train station, take a look around the station. Often times there are kiosks or booths set up that help you find a place to stay(Sevilla). Also there are often people looking for tourist to fill their hostals roaming around the train stations(Barcelona).
I've never had a problem finding a place to stay in any Spanish town and my Spanish is horrible. It would help to have someone to stay with your luggage though, at the station, if you have to wander around the station or just outside of it looking for a place to stay.
Have fun and relax and enjoy your retirement. See you in six-and-one-half years or less.
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"I swear -by my life and my love of it -that I will never live for the sake of another man, nor ask another man to live for mine."