Search Results: keep trying to get him back

Things he did:

1. When my a good friend of mine was in between us in class he would constantly tell him to stfu when he was talking to me
2. He used to make fart sounds with his hands, waiting for me to look at him and make my "are u serious" face to mimic me
3. He got very excited when I finally accepted to work with him once
4. He noticed I sleep a lot and called me sleepy head once when trying to wake me up
5. He literally humiliated himself on the class GC to try to get me to pair up with him for a presentation
6. He remembered my birthday when everyone forgot and reminded everyone
8. Called me once with his friends to ask me help for a work and after the called he said "bisou" (kiss in French) and his friends said "ah yes bisou" and he insulted them
9. Randomly coming up to me to ask me what game I’m playing
10. When I got a haircut he waited until my friends noticed it before telling me it looked cute on me, when I thanked him he puffed out his chest
11. He said a little pasta restaurant everyone goes to is shit but after he saw me going to it he started going there for lunch and when he sees me queuing he straightens up and looks at me
12. Once we had to correct our seatmate’s test and when I tried to give my test to my seatmate they turned back to give it to their friend so he yanked my test out of my hands and gave me his without asking
13. At the very second day back to school he immediately went up to me in front of the school door, I was confused and tried to leave bc he was in a call and it was awkward but he stopped me, ended his call and stared into my eyes while thinking about what to say before we walked to class together
14. Seems to have changed his morning schedule to arrive at school at the same time as me
15. At the queue for a small restaurant he got behind me and kept looking at my phone, talking loud about "interesting facts" (that were common knowledge) with his friend

I'm not sure if this guy in class likes me back so maybe you can help me figure it out.

A few things to keep in mind

• We sit next to each other, so a lot of what I see is from my peripheral
• We're 17, (I know It says otherwise I thought you had to be 18 and over to sign up so I made it older than I was)
• There was this one time when we were playing trivia in class and I was 1 point ahead of him and I think he was flirting/making banter because he basically said "I'll pay you to lose" or something like that but then after he said that he kept looking at me then down then back up at me and at one point he gazed into my eyes for like a good 5 seconds and I was kinda taken aback and made me a bit nervous.
• Another time we were doing a video project that required us to ask some of our classmates for help so basically he was going around the room asking everyone up else for help filming his video and every time he would sit back down at his desk he would look at me and when I would look at him he would look back at his laptop. When he did finally ask me he seemed a bit red in the face but it was kind of hot in the classroom so it could have been that.
• Sometimes my teacher likes to sit in the same row as us and grade work, so naturally I would ask her questions and when I would he would look at me while I was talking but I only would he look at me he would sort of guess into my eyes sort of dreamy like, (which I think is unnecessary like why are you looking at me right now focus on your work) but anyway

But at the same time I don't think that he likes me that way because sometimes when I talk to him he won't look at me directly : (

If he does like me back what should I do? Should I write him a letter? Should I try to talk to him more, I'm kinda playing hard to get right now.

Sorry for the long read, thanks for any help in advance!