Plumbing 101 from an Old plumber,
1) you can't have to many vents.
2) you can't have to many vents.
ok first point use a rv knife valve, a gate vale will not close if paper or any solid gets in the gate seat. better choice is a ball valve if you go residential parts.
A vent between the toilet and the rest of the system should do, preferably to the outside.
It sounds like your kitchen line may be a bit long. if over 5 ft. use a studor vent ( mechanical air vent) under sink.
Guaranteed if you flush with the outlet valve closed you will hear traps burp.
Yep I am new here and just starting my search for a bus.
This site has already been a great help, keep the info comming
Jeffro / Borday , whatever just don't call me late for dinner.