Search Results: asking if he''s taken

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!