Madrid is right in the center of Spain.
Yes, it is part of Spain.
Spain is in SouthWestern Europe, South of France, East of Portugal, and North of the Mediterranean Sea... Southern Spain is South of Northern Spain.
Spain is located in northern hemisphere.
Cadiz, Malaga, Cartagena, Seville, Cordoba, Granada, Jaen, and Huelva are all important cities in southern Spain.