yes if u want 2 fight him again
if you have beaten the league she cant battle you again
Actually, you don't ever need to set foot into the Cave of Origin in Pokemon Emerald after beating the Pokemon League ever again! There is no need nor no reason for you to be there anymore, anyways.
No, you dont see him again.
yes if you have any Pokemon that you want to evolve do the Pokemon league again and put an exp. share on the Pokemon
you can't. you can only fight the Pokemon league again.
journey again to achieve the another battle called the 8th gym Pokemon ruby
You can battle Wally a second time after defeating the Pokemon League.
Go to another place with Pokemon around about your chosen pokemons level and either battle them wild or battle a couple of strong trainers then when your Pokemon are a bit stronger battle the Pokemon league again
No you cannot. Your battle with her in front of the Department Store when you arrive in Lilycove is the last time you formally battle her. Other than that she appears everytime you defeat the Pokemon League.
If you are playing Pokemon Ruby or Sapphire, the battle at Lilycove City was the last rival battle. The same goes for Pokemon Emerald, but you can visit her again in Littleroot Town, where she talks about needing to find a lot more Pokemon for her Pokedex.
After you battle with your rival at the Dragon's Den he shows up when you're climbing the stairs to battle the Pokemon League again
Yes, after you beat the Pokemon league the second time, every time you beat the Pokemon league again red will reappear at the platform on the top of mount silver. But red's Pokemon will be a little stronger every time you re-battle him.