Can wizards/magic users possess more than one type of magic? I've noticed that in Fairy Tail everyone has a different type of magic. But would it be possible to possess more than one type of magic? For example: Natsu being able to use Fire Dragon Slayer Magic and and also being able to use Magic like Gray's Ice-Make spells? Or are there rules for his Dragon Slayer Magic not allowing him to use different kinds of Magic?
Yes, they can. The best example is Makarov Dreyar, Fairy Tail's 3rd and 6th master. He can master many different types of magics:


  
  Fairy Law
  Fire Magic
  Ice Magic
  Light Magic
  Maximum Defense Seal
  Requip
  Titan
  Wind Magic
  Dispelling Magic
  Telepathy 
  


Another example is Ultear. She originally learned Time magic and later learned Ice magic to kill her mother. Magic isn't something you are born with, it is something you can learn. So you can learn multiple magics, but with anything in life, if you stick to only one skill and train it with everything you got, you will become more profound in it, than if you divide your time between different skills.