i) Cadiz is a great destination for a day (or more), but I don't think it has any "wow" sights in the way Sevilla, for example, has. You might want to consider the cathedral, the Gadir archaeology site and (if open), the Roman Theatre. But, overall, I think the attraction of Cadiz is walking around the peninsula, enjoying the ambience and eating the wonderful food. Thus, strolling the narrow streets, coastal walkways and impressive plazas. Along the way you have specific places to visit such as the central market, Santa Catalina and Sebastian castles and Puerta de Tierra. If you want a longer day, you could include a brief ferry trip to Puerto de Santa Maria.
ii) Jerez is also great, but doing both on the same day would, I think, be too rushed.
iii) Usually you don't need to book in advance, but it depends on whether a festival is going on somewhere, etc.