For these examples, both can be correct, but with a change in meaning.
Mary said she comes from England. (Mary �s original country is England.)
Mary said she came from England. (Mary was in England and now she �s here, as long as here is outside England.)
Mary said she is American. (Mary is an American citizen and thinks of herself as American.)
Mary said she was American. (Mary was born in the USA, but moved elsewhere and changed her citizenship. She no longer thinks of herself as American.)
For the third example, both won or has won are correct and the meaning is very similar. In general, the simple past is used for actions completed in the past, while the present perfect is used for actions begun in the past but continuing up to the present. Present perfect usually includes a duration.
I worked as a bank teller. (Twenty years ago, and I no longer work at that job.)
I have worked as an ESL teacher for eleven years. (I started in 1999 and I still work at that job.)
I hope this answers your question.