Let's get through this systematically:
MP2 style duels (board theme): yes on a space, and yes to coin betting.
Later (MP3-6) duels: space is OK (though I'd prefer land on same space), and I think you should be able to wager 50 coins against a Star.
MP7,8,DS: I hate roulette wheels.
I think that the Duel should be chosen a la Battle Minigames in MP5-7 - three options, choose between them. If two minigames are chosen with one vote each, the third is played.
They could also devote a mode to Duels, which provides a welcome release from Battles Royales and Team Battles. A Duel game every turn - how fun. (though with more variety than MPDS's duel minigames =P)