as long as you can ensure that they are getting food, badis will do fine in many community tanks, however be careful about your numbers and tank size as males are territorial and even in a 29 gallon tank will still go after one another. They don't usually do a great deal of damage to one another, but they CAN, so make sure you have plenty of hiding places.
They especially like java moss, so the more of it you have, the happier they will be.
as for your tank in particular, i'd be leary of having them with so many big fish, but to be fair I know very little about those other fish. I would just be concerned that they would either outcompete the badis for food, or they would would make the badis food.