Your landlady is responsible for your fridge? That’s unusual. Or at least, it is in my experience in these down-under parts of the world.
Oh, the joy. I was awakened by the upstairs neighbours clomping up and down the stairs at six am. I counted. They were up and down 13 times. On the first day I haven’t had to get up to work or send my son to school. JOY.
I figured I’d take the time to do laundry and grocery shop - BUT I HAVE NO FRIDGE.
On the plus side, maybe your upstairs neighbour was up and down so many times because they’re taking a flyer on the rent owed and moving out. 
It’s now afternoon. I have no fridge. She told us it would be here this morning.
Riiiiight.
Do you still have the rotten food from the old fridge? Cus if ya do I can think of a few creative uses for it…
I have a spare room. And a FRIDGE. You and Dave and Buglet come live with me!
Oh, cats. Nevermind. 
I HAVE A FRIDGE!
About $%&#ing time. Sheesh.
But this business with the stuff coming through your ceiling from the upstairs apartment - in your position, I’d send her the certified letter per this page detailing the situation, so you can stop paying rent if you’re still there in 30 days. But I agree that the best solution is to get the hell out of there, as soon as you and Dave can manage it.
YAAAAAAAAAAY!