Hi,
I'm on H1B visa in Connecticut since 2005 and my wife is on F1 visa in Georgia (she has Graduate research assistanceship and her tax status is resident alien). My questions are,
1) Can we file tax jointly?
2) Do we have to file state tax separately?
3) What will be the best way to file tax in my condition? (married filing jointly or married filing separately) to get the maximum return?

Yes, you can file joint return as residents.
If you file as married filing separately, your wife will file non-resident tax return.
Read: Your U.S. Tax Return: The U.S. Visas

It is possible that filing separately gets the best refund tax-wise, but not likely.

It depends on your respective home countries and if there are tax treaties involved.