Dangerous?

I would not advise somebody else to do it, but have done it myself in a slide-in camper we had where the battery box was inside. No fumes resting or discharging noticed, but fumes when charging.

The 2 amps charging and fumes or not can depend on how far up the battery is in SOC, whether it has reached "gassing voltage" yet.

The fumes we got on charging set off the LP alarm, so that was another thing besides the smell. Based on those fumes, got AGMs instead for the camper, and now have them inside the Class C with the no fumes advantage (I do not overcharge them till they might vent!)

I don't know if the fumes are dangerous as such to a person sleeping, or if they would light off if any sparks or you use the gas stove top.
Might depend on whether the roof top vent is open or whatever. Probably a bad idea. So no-- I would not advise it.

Neither charged nor discharged, sure. I don't see any harm in that at all. It's an inanimate object at that point.
Being discharged, again, I don't see any problem with that.
Being charged, that's the one that has the potential to cause a problem. I doubt it would actual cause a problem but it's at least possible.