Most of your concerns are really pertinent and all are dependent upon how well the compost bin is set up and worked.
Safe composting (that is including any manure not just human) needs to be a hot compost with temperatures reaching a minimum of 150 degrees f for a minimum of three days. (I personally shoot for 180 f for five days in my manure heaps ).
If you are going to run a continuous addition compost bin for the purpose of processing human, dog, cat, pig, cow, horse, donkey, and any other animal you happen to think of (except rabbit) you need to only add in the center of the bin.
You will have to own and use a long compost thermometer to do daily checks (hourly would be superior) of the temp and you need a book to keep your daily log of the heap.
Having the right bacteria in the heap and knowing that you have the right bacteria in the heap is also a really good thing and easy to ensure since you can buy these bacteria as septic tank treatments. (Ridex is probably the most advertised of these products and it works very well for this purpose too.)
Containing any liquids in such a system would be (for me) a
common sense thing.
I would not want any seepage that might not have been fully processed into compost occurring.
Redhawk