I have 2 questions

1.- can anyone suggest how to approach a cash-register girl in the supermarket? I'd like to hang out with this attractive blonde, but don't know how to act in this case with the limited time given. What snappy lines would do the trick?

2.- I have this challenge at my dancing classes for a year now - there're several attractive girls from the advanced class (18-22 age zone, I'm a 26 yo beginner), that I've been trying to hook, but couldn't do more than few very short talks and cold reads that couldn't warm them much (the time for talks here's also very limited). I'm already out of ideas. I assume, using short witty phraises in the rare occasion when I dance with them - to make tham laugh - will warm them so that later I can naturally arrange to meet with them. Yet I can't think of such witty phrases. Could you help here?

Just have fun and be confident man, in both the situations there's no need for you to close straight away, which means that you can build your personality and attraction in the girls. There's nothing wrong with being completely honest and telling a girl you think she's pretty, or that you'd like to see her again.

The way I see it is; if you use lines and routines right now, they're going to mentally acknowledge you as the guy that's personality is made up of one liners, and when (if) they get to know you, you'll seem incongruent and unattractive.

It's not that I'm not confident... But when you're in a venue where you're stuck not knowing what to say, or how to approach - and despite your relaxed state the almighty doesn't give you any ideas - you'd look for some chat-up line examples to get you unstuck, so that you can come up with your own and feel sponatneous on the field.
(That's indeed how I got good at approaching in other venues) Unfortunately my ideas on approaching cannot be applied here where I have very limited time.
In the first case I'd like to say something that could get the girl off her regular way of thinking that I'm just another customer. Saying "How's it going?" and getting a "fine thanks" respond from her gets me nowhere.
In the second case even though I'm having fun I don't know how to express it with humorous lines or movements to get the girls laughing and attracted, and after a year of fruitless attempts I've gotten nowhere and am out of ideas.
What would you say if you were in my shoes?

I reeeealy wouldn't game the girls in your dance class man. If you succeed and then have a relationship which doesn't work out, you're gonna have to see that girl in class every time. If you try and fail, you're gonna have to see that girl in class every time too. Make FRIENDS with the girls at your dance class, treat them like they were guys, assume rapport, and LJBF them. Then you can socialise with them outside of class and they'll introduce you to their friends, who you CAN game. Plus, you'll get all that social proof from being around hot girls! It's win win.