Hi Claire & welcome to the board!
Here's a link to sleep training methods for toddlers: -
https://babywhispererforums.com/index.php?topic=63896.0Here's the link to help you with the choice of methods: -
https://babywhispererforums.com/index.php?topic=80750.0Both links are from the FAQ's so you might want to have a look at that as well in your own time.
Bottles at night - good that you have made a decision to take them away. You could also replace the milk with water and maybe put a sippy cut in the corner of the cot so if she is thirsty at night she can help herself.
To answer your q's specifically:
is 20 months too old for PU/PD? How long does it normally take a child of this age to improve
Yes, you would just do pd. THat all depends on your consistency and how tired she is. If you could please post your routine as well that would help. If she is overtired, I would suggest an earlier bedtime so that she responds better to sleep training. She might not fight you for as long. Can take up to 2 weeks. Try not to change your methods half way. Stick to 1 method and if its not working, re-assess and try another one in 2 weeks. Again alot depends on how tired she is. If she goes down ok for naps and bedtime that means she knows how to fall asleep. She might be having troubles sleeping throuhg because she has become dependant on the bottle to return back to sleep as well as being overtired.
I've been staying in the room while she goes to sleep as she cries when i go to leave and my book says you should stay there to earn their trust. When do I start leaving a bit earlier? when she's learnt to go off quickly with me there or should I start now so i don't become a prop?
The link I've posted will explain the GW method (which is when you would stay with her and gradually remove yourself).
What do you do if you're back is killing you from being bent over a cot for 2 hours?
Do you think dh could take over and give you a break???
From the times I've detailed, do you think my daughter is improving because it still feels really hard
In general it should take less time for them to nod off but there is regression which can happen even after they started sleeping straight through. Its just a matter again of responding the same way without any props.
hth & let me know how you go
Layla