Yes, BA207 to MIA is cancelled tomorrow. We will find out the reason for this, but it was an A380 and that sub-fleet (and its crew) are fully stretched with issues at the moment, so it will be either technical or crew shortage. The thread for delays and cancellations will tell you more on about Monday.

You are all entitled to EC261 compensation for the cancellation. This will come over as £260 per passenger. This is 50% of the full amount, see post 8 about the Azurair haircut, and in my view you should get the full amount since you lost a day of your travel with this. CEDR is the dispute resolution service here, they are inconsistent in applying Azurair. But the £260 per person should be paid swiftly.

The downgraded passengers get Mennens, see the wiki, but that should be about a quarter of the total cost of the ticket, very round terms, depending on the details There is a worked example in the wiki links, it's a bit complex, so you need to be on the ball to make sure you get the correct amount. This is payable by BA in law, but they may try to persuade you to get this from AA if you bought the tickets from AA.

The duff chair - that's a customer service gesture. Make sure you claim that.

The lost hotel spend counts as "consequential" loss and BA won't always pay that as a result. But put it in your claim, they may contribute something for it.

I am glad you got this sorted, but given an open hand it is better to arrive late rather than early. See the Signposts thread if it happens again (or put a post in FT, someone will give you advice very quickly).