tax questions

I have several questions regarding tax. Please help!

1) Filing status: My wife is working in MA and stay with my daughter for the year 2003 (more than 6 months). I am working in MI for 2003. As my understanding, my wife is qualified to file as head of household, which can save more tax. I have to file separately (married). Am I right?
2) If I am right, can we contribute Roth IRA for both of us? (our income is less than ROth IRA requirment.
3) What is definition for "did not live with your spouse any time at te year"?
4) For 2002, we filed jointly. Similarly as 2003. My wife was qualified as Head of Household. Can we file amended return for 2002? Amended tax return could not be filed from jointly to separatly. Is it OK from Jointly to head of Houshold?

Thanks a lot for your help!

Jian