Definitely the parent's responsibility to fit a stairgate if there is any risk of their child wandering around at night. Even with a working light, children can still stumble and fall when sleepy.
OP, without seeing the house it is hard for us to judge how serious your concerns are but to be honest, you seem to be expecting too much from your landlord.
And I'm still intrigued by the nature of the 'flammable substances' on the bathroom ceiling...
How is education supposed to make me feel smarter? Besides, every time I learn something new, it pushes some old stuff out of my brain. Remember when I took that home winemaking course, and I forgot how to drive? Homer Simpson