Is it normal to act awkward around girls i like?

Extraordinarily normal, especially for shy guys.

I think it's normal to feel awkward in those types of social situations. I can't relate to people that are completely comfortable with that because you probably don't know the person well, or if she's even interested in talking to you, and overall, you have no idea what to expect. Therefore, it makes sense why you would feel awkward.

Story of my life right here : (

I actually kinda like that! If someone is overly confident, or cocky I find it to be a turn off. If someone is downright pushy it disgusts me and shows a lack of respect. When someone is a little shy, and awkward, but works up the courage to speak to me I find that to be endearing, because it shows he cares enough to be vulnerable. Of course whether I accept him or reject him basically just boils down to if I find him attractive, if I get good vibes and we have stuff in common or not. I tend to feel most at ease with someone who's chill, a little vulnerable, but looks he'd still be cool if I said no. All you can do is try to talk to this chick and ask her out if she seems receptive. If you get rejected just accept it and be cool, it's not the end of the world.

I actually get really turned off when someone acts like they're doing me a favor or I ought to be flattered when they're hitting on me. There's a certain entitlement about it that I find distasteful.

Pretty normal.
It's okay to be sensitive. Sure, not all girls like that. But imagine if you could act super manly and confident. Sooner or later she'd still find out who you really are. So better just be yourself from the beginning.

Nothing unique about that!