Keep the Disruption Signposts thread (referenced upthread) handy for next time, it would have saved you quite a lot of trouble by the looks of it. In summary, it's best to book your own hotel from the get-go and to not assume you will get rebooked - that thread tells you have to navigate around this. There were flights before Wednesday, just not ones that BA were actively booking. I could see options on Sunday for example.

I suspect BA will pay the whole bill. Strictly speaking though, medications won't be included, that's really for insurance, and presumably is only a factor because you normally get free or low cost prescriptions? Usually getting branded medications in Dubai is a lot cheaper than anywhere else. But if the cost was modest, I've known BA to pay that. Toiletries, food, drink, taxis are OK, though for taxis they should all be to or from the airport. Taxis for other purposes would seem to be more for your own account. I would get photos of the various receipts and get a claim in soon. You can always add more receipts later via this link:
https://disruptionclaim.britishairwa...ditionalClaims