There are three holes in the tank. Toilet waste in 3" pipe, toilet waste out to dump valve 3" pipe, tank vent to roof vent 1.5" pipe.
Over the years there have been a couple of issues with either the vent pipe to tank connection or the vent pipe not extending through the roof completely.
Clean out as Dan suggested and keep on top of the kids until you have the opportunity to have it inspected.
No problem with the genny, that is what I do all the time. Genny has priority, so once running it will switch over.
When you do your monthly check, load it up with either the 2 AC's or portable heaters. Run for 20-30 minutes then turn everything off, no load for a 5 minute cool down.
BTW, that front cover on the genny needs to stay on when running. Contrary to what you may see others doing, the genny will not run cooler with the access cover off. Air flow is dependent on it being in place.