Does he like me?

Hey guys,
I really need to hear your point of you about the relationship I'm having with a guy that I knew recently.
So, we both go to the same school. in the first semester we never talked alone, we only saw each other with friends.

When the second semester started, he went talking to me. He invented that I had given him my school notes (cause we saw each other before an exam and I had on the table all my notes), but I was sure that I hadn't. In fact, I checked and I have them all. He just invented this story to talk to me. In fact, he kept on saying that he had my notes for all week.
The second week of school, we stayed together in the school hall during the lunch break, and we chatted a lot. He asked me some questions, like how old I was and if I had a boyfriend.
Later on, we didn't see each other many times, cause we're not in the same class.

I have to say, he's a guy who likes to be a little misterious, so everytime we see each other, he comes to me, he smiles at me, etc.

Btw, yesterday we spent some time together. We have the same passion for tennis, and I told him that I really like Novak Djokovic, so he asked me if I would marry Novak and I said that if I had known him at school, I would definitaley have a crush for him (lol). So he wanted to know why, what I like about him, his face, his personality, etc. He also said "do you like him more than me?", but he said that while I was talking, so I didn't answer haha.

Since he had to go, cause he had class, he blew me a kiss and told me to put it in my pocket to use in the difficult moments and then he told me to write him on FB.

So, here comes the question. I like this guy and I feel like his sending me many signals. The problem here is, why asking me to write him? I mean, if he really cared, he would have done it already.
I know I can be paranoid sometimes, but I'm not into games. What I feel is that his attentions are real, and he looks like a good guy, but that question really confused me.

Any comments? Any ideas? Anyone had a similar experience?
Let me know
Thank you all!