I don't think you can, i have been trying to figure out how.
You see Cynthia many times in Pokemon platinum. She gives you an egg containing a togepi in eterna city. She also meets you on your way to meeting and catching giratina. Also, if you defeat the elite four, you battle her for the title of Pokemon champion.
you can battle kyruem twice. if you fail to get him the first time, you can battle him again.
once
i bet them and Cynthia 5 times in Pokemon platinum.
Yes you can battle the elite four and the champion as many times as you want
Cynthia cannot be found in Challenger's Cave. You can find her in her Villa in Undella Town. During the first meeting you can find her in her Villa regardless of the season however after the first battle, you will only be able to battle her during the in-game season of Spring. Her Pokémon consist of Spiritomb, Garchomp, Milotic, Lucario, Braviary and Eelektross.
If you mean play AS her, You can't. If you mean AGAINST her, you battle her several times throughout the game
Yes you get the dark orb after beating cynthia 10 times
the only way to get to the fronteir brain in the battle dome in pokemon emerald is by beating the battle dome 10 times the only way to get to the fronteir brain in the battle dome in pokemon emerald is by beating the battle dome 10 times
You cannot catch Thundurus in Pokemon Black, he is exclusive to Pokemon White.
There are different forms of Pokemon and certain Pokemon you get to battle is at different times.
You will encounter N many times in Pokemon Black & White.