First we need to divide between continuous and discontinuous systems. Discontinuous systems are filled, digest and emptied. Lot of work. Pretty useless for a toilet.
Continuous systems are usually filled with water so that the entire environment is anaerobic. One the one side something goes in, while the same amount gets out on the other side.
So a flush toilet that comes with water is ideal because if you want to get the shit into the system water is the ideal transport medium.
The digestion process is not exothermic. It needs to get on temperature to function properly.
With the humanure of one family you are not getting far. There is not that much energy left in humanur. If you can combine it with compostable non-lignin containing material you will get far better results.
In my opinion humunur in a biogas system is always just an addition to the other stuff that you are feeding in when we talk family scale digesters.