Can/May

Are these sentences correct?
1. Sarah can dance very well
2. Can you swim? Yes,I can
3. Can’t she She can't ride,can she? 
4. Can he know,can’t he? He can't know, can he?
5. I have got a terrible cold. I can’t breath.breathe
6. Excuse me. May you tell me the way  Can you give me directions for the station,please?
7. May I borrow your dictionary Bill?
8. Can you buy some fruit? Yes of course,mum
9. Excuse me,where may I find a bikini?
10. I can’t believe this pullover costs so much. He It can’t be soo expensive!
11. Can be Peter arrives late. Peter might arrive late.There is a bus strike Bus drivers are striking.
12. What bad day! Can snow in the afternoon. It might snow in the afternoon.
13. Alan can might be at home
14. Cell phones may not function in this zone
15. Give to Mary my phone number to Mary. It can be she hasn’t it She might not have it
16. Only licensed people may use this enter entrance
17. Students may not park their mopeds in this zone
18. Excuse me,May I sit here? Yes,of course
19. Can I go out,mum? No you can’t

Can/May

Are these sentences correct?
1. Sarah can dance very well ok
2. Can you swim? Yes, I can. ok
3. Can’t she ride,can she? > She can't ride, can she?
4. Can he know,can’t he?> He can know (about it), can't he?
5. I have got a terrible cold. I can’t breath. ok , but  you cannot say that> I have a cold . I don't feel like talking /I don't feel well etc.
6. Excuse me. May you tell me the way for station,please? X Could you tell me the way to the station?/ May I ask you (to show me) the way to the station? May I = To request for/to do something> May I sit here?/ May I borrow your blanket for a while?
7. May I borrow you dictionary, Bill?
8. Can you buy some fruit? Yes, of course, mum
9. Excuse me, where may I find a bikini?> where can I...
10. I can’t believe this pullover costs so much. He  It can’t be soo expensive! ("it " refers to a thing, "he" refers to a guy)
11. Can be Peter arrives late. XX There is a bus strike > Peter may/will arrive late .....
12. What bad day! Can snow in the afternoon.> What a bad day it is today . It is even snowing in the afternoon !
13. Alan can be at home . ok depending on context > Allan can be at home if you want to see him there.
14. Cell phones may not function in this zone > Cell phones may not have coverage in this area/place
15. Give to Mary my phone number. It can be she hasn’t it> Give Mary my phone number . It seems she hasn't got mine.
16. Only licensed people may use this enter> Only authorised people are allowed to use this entrance.
17. Students cannot/ may not park their mopeds in this area/place  zone
18. Excuse me, may I sit here? Yes, of course
19. Can I go out,mum? No you can’t > May  I go out ? No, you may not. ( "Can" is an ability to do something, so I am sure you can do that, that to go out. " May I " is used  to ask for permission . Of course, you can , but you may not= Of course , you can , but you don't have my permission.