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.

careless - usually used to indicate that (sufficient) care was not taken. He dropped yet another vase. He is definitely carelss. He let more rabbits into the garden. He's careless about his duties. carefree - he has no cares, no worries, no concerns - A statement of their personality. Married with a mortgage? No. Not him. He is single and carefree. phantasy vs fantasy - yes I'd take these as the same, but I suspect phantasy is less common, now. Google gives me for Phantasy noun variant spelling of fantasy (restricted to archaic uses or, in modern use, to the fields of psychology and psychiatry).

Tim has given a good answer regarding "careless" and "carefree." "Phantasy" is an old-fashioned spelling of "fantasy." No one uses this spelling anymore. You may see it if you read novels or other books from the 1700s or 1800s, because it was a more popular spelling at that time. You will probably never see this spelling in a modern text.