It's so cute. A real AFC emerging from his cocoon.
To be young, inexperienced and insecure. Enjoy it while it lasts.
Be careful being to PUA about this. You're using a guidebook in a language you don't really understand, so be careful trying to follow too closely.
First, try to avoid being so formal. Don't ask a girl on a date. Just go out. Making a date puts all sorts of stupid formalities in one's head (like paying and owing a guy a kiss on the cheek for paying).
What you did wrong here (which is not really wrong, but really normal) is being insecure. If you are bowling and she is into you, then for God's sake man, escalate. The interaction with bowling is difficult, because you are constantly switching places. It's fun, but if your kino is a touch on the back between rounds or a high five, well, that's not really kino, that's buddy contact. I did go bowling some time back and my kino was just unceasing assault on her ability to get the ball down the lane. In general, I wouldn't go bowling though.
Next, don't take girls to dinner. Being physical across the dinner table at most restaurants is nearly impossible. I usually have to push the entire table setting to the side so I can get a girl. Also, you are showing your chest to her the whole time, which is a no-no. You can be witty and charming, but as there is no physical escalation it's hard to make it sexual. So don't do that.
Another clue to your insecurity is your confirmation seeking to see if she liked you (that's what I found totally adorable). Was your plan to escalate to hold her hand in the theater? Hmm.
My advice: relax, mate. You're fine. Try to do activities where you can be near her and get touchy. When you make her laugh, gently hold her forearm. Tell a joke that requires you to touch her hair. Make her laugh with some story about dancing where you have to bring her next to you like you would in a waltz.
Try to avoid dates, just hang out. Try to avoid formalities. If she accepts your physical advances don't be a puss and kiss the girl. Go for little kisses then bigger kisses. It's a fun learning process, enjoy the ride.