Hello Gouzai, The noun "aim" needs to be defined so number 3 is out of question. The indefinite article 'a' is not properly used in this context . The aim is the intend or the point and it is already a defined concept,unless you ask to mention one aim out of many. The more appropriate sentence is number 1 ,where you use the definite article "the".

Yes. Though I think the last sentence isn't grammatically correct. (You can make it correct by adding "the" or "an" in front of aim...but then it is the same as the first/second sentence so...) The first sentence emphasizes a specific aim of education. It's like saying "What is the purpose of education?" or "What is the reason we have education?". The second sentence asks what is one aim or purpose (out of many) of education. Of the two, the first sentence is more common. I realize the differences between the two sentences is kind of subtle...so I'm sorry if you find this confusing. I hope this helps. ^^