*Do you think are these correct social expression?
Hi, bear_bear: You can say, "Are these correct social expressions?" But if you begin with "Do you think," you can't use inversion in the actual question. You must say, "Do you think [that] these are correct social expressions?"
1 A: (i) Can you play badminton with me?
(ii) You want to play badminton?
B: Sure. Let me get my racquet.
Yes, those are OK in informal English. Speaker A can also say:
- Would you like to play badminton with me?
- Can I interest you in playing badminton with me?
- How about a game of badminton?
- (Do you) feel like playing badminton?
2 A: Do you want some more chicken?
B: (i) Sure. / Yes.
(ii) Sure, thanks, mum. / Sure, Mum. / Sure. Mum
(iii) Sure. Give me 1 more chicken.
(iv) Sure. I want some more chicken.
Yes. But in (iii) you should say "1 more piece of chicken."
I prefer "I'd like" to "I want" in this context. Also, please note that "one more cheese sandwich" implies that you have already ordered a cheese sandwich, though you haven't mentioned it in the context. Lastly, instead of "May I take your order?," you may, depending on the context, also hear "May/Can I help you?," "Are you ready to order?," etc.