I had to look up phantasy because I've never seen it used, but the dictionary says it is just a different spelling of fantasy. So they mean the same thing.
Careless and carefree mean different things.
Careless means to not be very careful, especially when you should be. A careless person makes too many mistakes and may hurt people or themselves. Or it may be they make simple mistakes like spelling, etc.
Carefree means someone that is light-hearted, free spirited. People often say a similar phrase, "he/she doesn't have a care in the world". A carefree person loves life. A carefree person may be careless as well, but saying they are carefree doesn't refer to them making a lot of mistakes or hurting themselves. Sometimes carefree can imply they may hurt other people, but mostly emotionally by leaving them and moving on.