Hi Carl,
Using a gas stove or oven in a small space like a trailer is not great for your health unless you vent it somehow.
The best option is a thru the wall powered fan/vent, or a ceiling vent.
Some people simply open a window or two and don't worry.
That method is good in the summer when the door and all the windows are open, but when it is cool, or very hot and the heater or a/c is on and the windows are closed, it doesn't work very well.
Having a dedicated vent fan near or over the cooking area to draw the exhaust and cooking fumes out, just like at home, is
the best bet.
If you are talking a stove in a teardrop with the typical open galley, no, you do not neet any special vents.
Having the hatch open while cooking (and during cool down) is pleny of ventilation.
I am not a fan of heaters that are "ventless" as exhaust fumes, no matter how safe the manufacturer claims they are, are still "exhaust fumes".
The resulting air you are breathing all night long while you sleep is simply not the same as fresh outside air.
To determine what clearances you need, you can look up the specifics on the heater you are interested in by typing the name and model number on the Internet.
Rob