All you gotta do is tap the badge icon in the edit team section (positioned above the leader). You can switch badges anytime you want and there's no cost to switching. You can even have all teams using the same badge.
Atm, there's no badges that increases orb drops. Besides the 2 already mentioned, there are: +100 cost, +1 sec move time, all attacks = mass attacks, 25% RCV, 5% HP, 5% ATK, +1 SB.