What did you use to combine the outputs? My guess is that's where the noise problem could be.
Unless your already using it for something the GL2400 has mono output on an XLR, is labeled M on the back next to the main left and right outputs, the level for that mono out is the right hand of the three yellow faders in the master section.
Using the group out will work, as you found you need to depress the 3-4 button on the all the channels you want to be in that group. If you are only going to use groups 3-4 for your broadcast feed you will need to keep the LR buttons push on all of the channels and above the the group 3 and 4 master faders pan control is a switch that says group to LR, on group 3 and 4 you will want those two switches in the off or the up position. With those two switches off/up any level changes your make with the master group faders will not be factored into the main LR mix for the sound system.
For normal grouping operations you would depress either the 1-2 or the 3-4 buttons while having the LR button in the up position, then to individually select one of the four groups you use the pan control, turning it to the left selects either 1 or 3, to the right selects 2 or 4.
For what you doing the way I previously described is what you want to do to use the group outs.
Using the mono out gives you another option at the press of button. If your are not using aux 6 for anything (if you are maybe it could be moved to another aux) you can create a sub mix for your broad cast using the aux six controls (make sure there in the post fade position) start off by having all of the aux six controls set the same maybe about the one o'clock position. With the aux six in the post fade position and all the aux controls set the same the mix that comes out of the mono output will be the same mix balance that is on the main L and R outputs feeding the system, now let say that on the mix going the broadcast the pastors mic sounds lower compared to everything else go to the channel that the pastors mic is on and turn up the aux six control higher, that way in the mix going to the broadcast the pastors mic will always be at a higher relative level to everything else on that mix. Anything else that you hear on the broadcast mix that is either too high or low can be adjusted as needed using that channels aux six control.
And now for the magic button you need to press to put aux six into the mono output. It's a small recessed switch through a square hole above the R master fader, it says M source, you need a small pen point to push the switch down into the aux six mode. When the switch is up the mono out is a summed mix of the left and right outputs, that mode will work as well for you only yo do not the aux sub mix option.
As for you other issues, that's another topic for another time.