I am a Spaniard flying in the Uk and originally from BCN. I can answer a few of your questions:
- income tax: I am not an expert but I am 99% sure you will have to pay income tax in Spain. As others have suggested, the system is quite similar to the UK one, taxes a bit higher (especially "Seguridad social", which is our National Insurance).
- schools: it depends on how much money you can spend. I would not recommend public schools. Private schools are really expensive, but you will find that they are very good and British schools have got loads of good reputation. "Concertados" schools are very good as well, and they are normally paid 50/50 between you and the Spanish government. A rough idea about prices is: private 500-1000€ a month, concertado around 300 and public schools are free.
- language: somebody complained that you need to know Spanish for almost everything, especially dealing with the government. Well this is the case in every single country in the world. Go to France and try to speak English, go to China and try to speak English. I am Spanish and I don't use Spanish when going to hospitals in London or speak to the DVLA. English is used as the international language in many areas but it's not an official language in many many many countries, so you will have to get used to that. As somebody said, your children will learn Spanish very quickly.
- health system: I thought the public system was rubbish, but having suffered the British one, I would say it is not that bad. However, I would strongly strongly reccomend to have a private medical insurance, which is a bit expensive but worth it. Private hospitals and doctors (at least in BCN) are extremely good, and the overall statistics for illnesses like cancer beat the ones in the UK (which are fairly poor to be honest). The private health system does not go through our GPs (as it happens in the UK), so they are extremely quick, with a good cover you will be seen by an especialist within a week. A good medical insurance can be around 50-80 euros a month if under 55 and expect double of that when older.
- areas: BCN is a fantastic place to live. You will not find many brits here (although you will find that many people speak English, especially young people) but there loads of people from different countries. Good schools, good hospitals and loads loads loads of things to do. Fantastic beaches close by and even ski resorts. We have got many many flights to the UK every day, which is a bonus (EZY, BA, RYR, Norwegian, MON, VLG, Jet2...). If you want to find brits, you will need to go south (Malaga being the best one).
- buying and renting: as somebody suggested do not buy before renting. It is not only the paperwork, it is the fact that you will need to know the area. Tourists are normally atracted by areas that we hate. Living in the centre of Barcelona (Born)- and many cities - is a nightmare, and the other day I watched "A place in the sun" and people were desperate to find a house there! Know the city before deciding and know public transport, which is fairly good and much much cheaper than in the UK. Having said this, properties are now very cheap in Spain, so it is a good moment to buy.
- weather: ... that's the reason why I am part year working and enjoying the winter over here!
Finally, deciding where to live is extremely important. Different areas in Spain have got different personalities and culture. Catalonia is very "European", people are switched on, hate bull fighting and flamenco, but they speak another language (Catalan), which you must take into account. The South (Malaga, Sevilla) is very laid back and passionate for what Catalans hate. Madrid is something in between and the north is just quite similar to the UK weatherwise.
Good luck, Spain is a fantastic place to live and you will find there pretty much everything you need (except for Cadbury chocolate and good lemonade).