Here by term "natives", you mean to say those who are more proficient in speaking English language, right.
Now, the usage of terms you have mentioned:-
1) it depends whether you just say "congratulations' or say "congratulations for winning" in the manner you are carrying out the conversation
2) Since tea is always served in cups or other standard measures, you always order for "two cups of tea". two teas please is colloquial language where cup is understood, but not a proper Engllish sentence.