You should pay of course, since you invited her... but if she insists to pay her part you should say:
- Let's do it this way, i play this one and you pay the next one (it solve the problem and make possible the next date!)
The best advice i can give you, don't waste all of your day walking, how would you be able to create a moment if you are walking? You have to be in a place for as much time you think it's comfortable to be! And on that moment you should talk, tease, touch, do stuff!
Also choose the place to make sure you can sit next to her instead of in front of her! For example choose sofas, they are comfortable and you can seat next to her.
You can try this, i let you use my weapon if you want to.
Before kissing her just look at her and say:
- Sorry but I've lost a lot of opportunities because i didn't try... then put your hand on her face (over the hear), push her to you and then kiss her.
If she refuses, fuck that, go away and leave her where she is
I hope that when you quote me back on this forum you would be able to give me good news

Best of luck!