I saw the best results when using multiple strains of bacteria, ie hydroguard and orca together, so I would not say they fight. Before I got my chiller, my res got awful hot like 80 and I did not have any problems. Made me wonder if I even needed the chiller but anyway...
As far as the tea, I think the Hiesenberg receipe may the most accepted, but again I urge you not to use the tea unless it is absolutely your only option financially. I simply dislike the idea of putting anything like molasses or sugar in my res, much less having been brewed.
Other bacteria will certainly feed off that food source, and they may not be bacteria you want. The bacteria you are adding are bacteria that naturally colonize roots and develop a relationship with the roots of the plant, so in that regard, why feed them anything at all?