I think I'm falling for a girl and maybe she is too.
But how to be sure and how to make her see I like her without telling her too directly?

Thank you

If she lets you date her chances are she is interested.

What talaniman said is true, but sometimes its hard to you know, see if they let you date her. There are ways to tell, by body language mainly. A couple I know are if you walk into a room and she changes her posture. Or if when your talking to her or near her she adusts her clothing or her hair or something. Easy way to get a better list, youtube: how to tell if a girl likes you. These aren't always 100% though, so be careful

Casually talk to her and make eye contacts at some point.