when you see your rival first you battle him and then he will go away.
you see him throughout the game
when you are about to battle the elite 4 you walk in the door and you see your rival. Then he/she challenges you.
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You go up
NO
After the Dragon's Den (when not battling Lance), you can find your rival at the Pokemon League on Mondays and Wednesdays.
go 2 spear pillar
7, i believe.
Your rival will have it at som point
You first see him outside of Prof. Elm's lab, then you see him in Cherrygrove, from there on its random
No trainer, other than your rival, will have a starter Pokemon. Thus, if you have a totodile, and your rival chooses a chikorita, you will never be able to see a cyndaquil through normal game play (e.g., not trading).
Type in "Rival customer service" on your search engine and see if they are still alive.