The rules on residencia cards in Spain have been changed recently, and if you are an EU citizen and you have a job in Spain - either as an employee or as a self employed person - you do not have to apply for a residencia card. If however you are from outside the EU or if you are retired/unemployed, then you should apply if you stay in Spain for more than 6 months.
The EU reciprocal agreement covers you for treatment in Spain until you get an official Medical Card (Tarjeta de SS) from your local Social Security Office (INSS – Oficina del Instuto Nacional de Seguridad Social) in Spain.
An NIE number is essentially a tax number for foreigners in Spain. You need one if you are going to buy a house or a car, if you are going to work for a Spanish company or if you want to apply for residencia (a residency card).
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