No you get the badge by beating them, and can battle anyone at anytime.
Ex: Water, Ground, Bug are a triad. You beat Bug with Gyarados, Scolipede, Charizard, Mew, Venusaur, and Salamence.
You'll then have to also face the Ground & Water Leaders using that same team.
Now, If you somehow cannot beat them the remaining Gym(s), you are allowed to change your team around, but at the expense you'd have to re-battle the Gym(s) you've beaten.
As for the Triads, this League almost works like how Trinity does. There are 6 Triads each containing 3 different types in it. The goal for Challengers is to beat all 3 Leaders in the said Triad using only 1 Team.
As for the rules, that list I would have to say is outdated.
it got changed around we now have triads which you have to challenge leaders now in 3 which dj can explain it you feel your confused I would give a huge explanation but on for a short time atm and yes your badges got reset because of the new rules but no worries
Well, you never know until you try. Lots of us haven't been having challengers, so I'm sure we'll need practice too. I know for sure my Gym Teams aren't perfected like I try to do with my Regular OU Teams. Plus most of us are now just waiting for Sun/Moon to see if activity will increase again. Until then, we're just battling amongst each other for fun. Using Pokemon we rarely see used.
Hey, I sure do remember you alright. Hope everything's getting better.
The League Section is moving slowly at the moment, for TEF, I do believe they've reset the League which caused the changes to the rules, and that means everyone had to restart in badge collections. There are a couple open positions as people either lost interest in playing Pokemon, or had real life problems to sort out.
To gain entry into the Elite 6 Council, you just need to win 8 Badges at the moment. And as for Challenging Gym Leaders, you're allowed to use any OU Team, but once you beat a Gym Leader in a Specific Region, you must defeat the other 2 with the exact same team. Any Pokemon changes made to the team after you've earned 1 badge, would result in you having to re-battle that Gym Leader.
There are also some Gym Positions open for grab if you wish to become a Leader, just apply like you'd normally do.