When was the first international T20 match played, and who were the two teams ?

Answer 1

17th February, 2005 between Australia and New Zealand
The first international T20 match was played on 17th February, 2005 between Australia and New Zealand at Eden Park, Auckland.
The first ever T20 match was played on 13th June, 2003 between Durham and Nottinghamshire at Chester-le-Street.