the first duel didnt finish because alexis told everyone the campas were coming and if they got caught they would have been expelled.
After you get your first duel spirit, you get to duel him. There are also some other times after that where you duel him
Episode 8: For the Sake of Syrus
Jaden wins
Jaden Yuki duels Kiaba man in episode 34
yugi moto
Yes, throughout the series the creator has been dropping hints about Alexis' feelings for Jaden. Jaden made a good impression with her on his entrance exam to get into duel academy, by beating Dr. Crowler and later on gained more of Alexis' affection by beating her and Chazz in a duel.
you can duel him in story mode a few times but after you beat the game you can find him on the island somewere.
Space Duel happened in 1982.
Duel Love happened in 2008.
Air Duel happened in 1990.
Last Duel happened in 1988.
Artillery Duel happened in 2600.