Does he like me?

So… there’s a guy who I have a crush on in fencing. (I’ve never had a crush on anyone before either so this feeling is really new to me). He’s a very polite, handsome and a sweet person. He smiles a lot but is also quiet like me. At first, we kinda smiled at each other during our practices and then slowly we started saying “hi” to each other and now we fence each other regularly (he has a high rating in fencing and is one of our top fencers on the team). We now normally text each other about stuff related to school and fencing. There have been a few situations that have caught my attention with the guy though and I’m not sure what to do. Five scenarios have happened thus far since the beginning of the semester:
1. He always critiques my matches with other teammates, but when it comes to watching other people fence, he never critiques them unless they ask.
2. Once we had a fencing team dinner and he sat next to me. He was constantly on his phone, but when I started a conversation (with him or another teammate) or when someone asked me a question/conversed with me, he’d set his phone down and look at me while I’m talking. If someone else talked to him, his phone would be in his hand.
3. He’s always standing next to me when we’re in a group. And sometimes he would look at me for a second, and if I feel him staring at me, I look at him but he quickly looks away.
4. Recently we had a fencing competition. He was by my side during all of my matches cheering for me, getting water for me, coaching me, and telling me to stay calm and telling me that I was doing a good job while patting me on the shoulder. He didn’t cheer as much for our other teammates though…
5. After the competition, both of my swords broke. So then during our next practice, instead of fencing, he worked on fixing my swords with me (since he knows how to fix swords). I have never seen him fix our other teammates’ swords before, and he was super insistent on fixing my swords.

We give each other high fives and hugs often, but I feel like that’s what friends do though.
(He did touch my hand once (not in a creepy way or anything… it was more of guidance for an action in fencing, but I felt my heart thumping like crazy).) And I also realized that when I’m near him, he’s always running his hand through his hair…

Some friends and I are hanging out soon and I invited him. And he said “Sure!!” (This was by text.)

I don’t know what to do? I was always told that the woman should never ask the guy out… But should I say something like “hey, I have a crush on you?” or “I like you?” Some of my friends said that he is definitely interested in me (but what if they’re just having fun watching the guy and my interactions)… My main question is does he like me?