Are they sash windows? If so you can fit stops so that they can be opened enough to let air circulate but not enough for child to fall out. They also prevent the child from opening the windows. All our upstairs windows are floor height but this has solved our problems. We fitted bars in our previous place but children thought they were ladders!
re: fittng new glass.........we've just put some windows in our property and had long discussions about one which is very low down. if it had been about 5cms lower we would have had to install that safety glass with the wire in it. as far as i'm aware it is a legal requirement on a window with a sill lower than 80cms from the floor.
this would only apply to your window if the glass was broken and needed replacing.....its perfectly legal as it is now.
definitely approach your landlord and see if he has any thoughts about how to resolve it.
I believe I have seen window stops for hinged windows somewhere, they are used for some double glassed wiondows. They allow you to open the window but just enough to avoid a baby comming through (about 3 inches).
Don't use the stapple gun, if your baby falls onto the chicken wire the strong enough to hold his weight.
How old is your child? would one of those travel starigates would do? they can not be opened nor climbed, have no bars and are cheap.