Haribo, welcome to TP. There is such a lot of good advice, information, and support on here.
I'm sorry as I've not read your post as thoroughly as I might have, and this is a bit rushed. I am sorry to hear about the situation with your mother. You have a lot going on and the hospital is clearly not communicating with you well at all, which makes everything harder. I am sorry.
I want to say that you should not beat yourself up for feeling overwhelmed, especially as you've been a carer before. Sad facts about dementia (Alzheimer's or any other type):
-it will get worse over time, but nobody can predict exactly what will happen or how long it will take
-it does present a lot of challenges with daily living and behaviour
-in addition to the symptoms a lot of us know about, like memory problems, there are things not all of us know about ahead of time: delusions, sundowning, agitation, sleep disturbances, incontinence, eventual inability to learn new things, problems with UTIs, et cetera.
There is a lot of good information available from the Alzheimer's Association. When you have time, which is probably not right now, you might explore their website.
Another thing you should know right now about dementia is that it will eat as much of your time and energy as you throw at it. You can budget your time and energy and get help, or you will spend an awful lot of your time dealing with it one way or another, in ways both big (medical appointments and emergencies) and small (too many to mention).
I hate to be the voice of doom, but you are right to be concerned about taking this all on.
Don't lose sight of the fact that you are important, you have a right to your own life, and in the UK, you cannot be forced to be a carer.
Having said all that, and if I haven't totally frightened you off, some details.
While I am in the States and have a very imperfect understanding of how a lot of things in your system work, I do know that you should be able to ask any nurse or staff member at the hospital for a list of your mother's current medications. You can politely but firmly ask, and just stand there until they print it out and hand it to you.
I would also not agree to your mother's discharge from hospital until they have a discharge plan in place and you have clear information, in writing.
If you don't already have PoA, get on that, because you are going to need it.
In the meantime, I'd contact her GP and although they may say they cannot talk to you without your mother's permission, you can talk to them. Tell them what is going on and see if they can get written or verbal permission from your mother to talk to you. A helpful GP will know how to do this.
I'm not sure how you arrange visits to the house from OT and the falls team, but someone here will know. This is important for her safety. The stairs are a huge hazard and the OT/falls people would have suggestions about that, I am sure.
Don't beat yourself up or feel guilty about not being good at patiently sitting there and listening to the repetition. It's enough to drive a saint mad in minutes! If you are more comfortable with the paperwork/administrative side of things, give yourself credit for that. It needs doing and it is still caring for your mother.
Don't forget about support for YOU. TP is a great resource. There are also carers cafes and support groups and you may want to find one of those in your area. It can help to be with other people in a similar situation and have a coffee and a chat. You might also tell your GP what is going on.
Finally, please do try to be as kind to yourself as possible, and sleep and eat properly and so forth. Also please remember that the enemy here is dementia, it's not your fault, you've done nothing wrong, and you are not a terrible person.
Best wishes to you and your family.