The Pokemon league is where after you win 8 badges, you get to battle the elite 4 (four tough trainers) and the champion of the region (in diamond it's Cynthia until you beat her).
the best Pokemon for the Pokemon league is definetly latios
In Pokemon League
beat the league and he will be gone
there are none that i know of in diamond. sorry(-_-)
I beat the league on Pokemon Diamond version, and there was no cave involved, if that's what you were asking.
near the Pokemon league
beat the Pokemon league
There is a road behind the Pokemon league where Shaymin can be found if you get Oak's letter.
She stays in the Pokemon League.
No
You can get it in the underground after the national dex which you get after the Pokemon league
beat the Pokemon league