no he is not. the champion is Cynthia not your rival
You don't need to defeat the Elite 4 20 times, your rival is at the Fight Area every Saturday.
when you are about to battle the elite 4 you walk in the door and you see your rival. Then he/she challenges you.
If by strong you mean higher level, the stronger trainer is your rival, which you can battle at the weekends at the Fight Area.
After 20 wins, your rival's Pokemon level up.
When you go to Stark Mountain you will meet your rival (you won't battle him/her). After that you will be able to face him at the Fight Area on the weekend(Not on Friday).
resort area
at the battle area after the elite 4
kill the elite 4 noob
at the elite 4 before you fight them. in the afternoon.
there is no last time
You need to get the Pokemon that are super effective against the Elite Four and Gary, (your rival) the champion
No, you do not have to beat the Elite 4 to get the National Dex in Pokémon Diamond.