Which ones of the followings do you say?
1. Would you like some tea?
2. Would you like any tea?
3. Do you have some tea?
4. Do you have any tea?
5. Can I have some tea?
6. Can I have any tea?
If there is any differences in use between them, plea enlighten me. Thank you!

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A native speaker is most likely to use 1 and 5, to refer to wanting to drink a cup of tea.

Correct statements with 'any' will be:
There isn't any tea left in the pot.
Is there still any tea left in the pot?
I'll have another cup, if there's any left
Do you have any tea? to ask whether there is any tea left or not because I am not sure.
Do you like any sort of tea? If you are having a a tea-discussion.

Furthermore:

''Would you like any tea'' is wrong because you are asking the person if they would like some tea which means there is some tea left. Obviously, you wouldn't be asking the person if there was no tea. When the question is positive, use 'some', therefore, ''would you like some tea'' is correct.

Goes for the other positive/negative sentences in your example, as well.