I'd like to answer your question about what goes on inside the 'casetas de Feria', since I was born and raised in Seville. As it was explained before, most of them are private and paid by: families, clubs, associations, or businesses for their members and/or workers. They are also places to invite friends and clients alike and it gives prestige to the sponsors. It is convenient and helpful to know people 'with casetas', so that you have several places to rest, eat and enjoy the atmosphere.
The caseta is usually divided in two rooms. The front room, with a 'tablao' in the center or on one side. This tablao is used to dance 'sevillanas', our traditional dance. People of all ages come out to dance and show their art. Around the tablao there are numerous tables and chairs. Sometimes, the dance music and singing is recorded and played loudly throughout the day or it may be sung and played live. This usually happens in an expontaneous way, among friends.
The back room is usually less noisy and crowded, depending on the time of the day. There is always a bar that serves cold drinks (Jerez and Manzanilla wines plus local beer are typical) and tapas (cured meats such as jamon, caña de lomo, as well as seafood and the traditional Spanish omelette). Prices are usually high during the week of Feria, so familes are known to bring their own food to the Feria (at least until 20 years ago).
I hope this gave you a little more insight into one of the best known Spanish traditions, the 'Feria de Abril de Sevilla'.