I'm 16 and really confused, there is this shy guy who I think fancies me but I am getting mixed signals from him.

It seems a bit weird giving my opinion to a 16 year old, but really I remember those days too, where I had a crush of people in my college class and couldn't stop smiling or keeping my eyes off them.  It's a bit cute, now I think about it.

I had a feeling that he was staring at me from the science table but I looked and he seemed to be looking elsewhere. In English he put his hands out without saying anything to put the books away (which I had in my hands and did not know where to put them) When Miss said my name and he looked back at me whilst I was talking back to my teacher.  Another occasion where he seemed to be staring at me would have been in Maths. In the hall and in I.T, he was facing towards me. In English, when Miss was about to read work out,she was standing near me and he was totally looking in the direction of Miss. In English when Miss called my name out he looked back.  In one class lesson he was right behind me. 

It seems that he is at the stage of checking you out but not ready to ask you out yet.  He's trying to assess you, whether you fancy him, whether he's likely to be successful, he obviously likes the look of you if he keeps looking at you. 

In Science club he stated let’s stay here to his friends where I was. His mate said my name for his name.

There's an obvious hint there, his friends know he fancies you.  That is just a giveaway.

But he does not really look at me when I am going past him or if I am close to him.

Do you think that I'm just being paranoid and reading too much into the situation or do you think he fancies me?

He fancies you, but he's not decided yet whether to make a move.  So he's either not sure he fancies you enough yet, or not sure whether he would be successful, if he asks you out.

P.S Also, I am falling for this guy, I never liked him at first but when he started staring at me and stuff,I started having feelings for him. I really need to know does he fancy me (without asking him) and there is only one more day of school left!!!

Unfortunately I'm a day too late replying to this.  But I suspect it was too early for him to ask you out anyway.  So if you see him over the summer holidays, maybe it would be good if you could persuade him to include you with his friends when going out.  So that you can get to know each other more.  Or even that you could tell him you are going out with your friends and he's welcome to join you.