Unfortunately Sarah this is a process that you will have to go through in order to have your claim assessed. The system is in place to try and persuade claimants away from claiming - they have proven statistics that show that the harder it is made to claim, the more likely people are to abandon their claim. Sadly, this means that people with genuine mental health issues suffer in the process. This is because there are far too many people crying Wolf claiming mental health conditions that they just don'thave and they think it is easier for them to increase their benefits.
So, you will need to gather up your strength honey and ask for help from your GP and CAB - let them share the burden of this process - the CAB are used to these claims and will have far better insight into how to help you than you have doing it by yourself. Your GP should be able to support your claim with details of how long you have been ill (ie., from when you were first treated and medicated), what meds you require etc.
Try not to worry - at least now you have a payment agreed and I would just call them and see when it is likely to be paid. I dont think it should be that long now that they have notified you.
With regard to your sleeping pattern - this is absolutely no good for your long term mental health - you need to sleep at night and have get up during the day and potter around (at the very least) - why not ask your GP for something to help you sleep? Your body clock is all over the place - did you know that night workers are more pre-disposed towards depressive thoughts than day workers? There is just a chance that if you could regulate your sleeping pattern, you might start to feel a little better.
Good luck