Does anyone know what kinds of taxes are these, and how could I tell if they are non refundable before I book, such as on my LHR-MAD ticket? Would it depend on when I cancel the ticket, such as, canceling on the day of travel might not receive a refund of the UK APD or PSC tax?
For a flight like LHR-MAD you should get 100% of the taxes and fees refunded when you cancel. With all awards booked through AA it doesn't matter when you cancel as long as it's before the scheduled departure time of the first flight.
I'm sure there is some obscure tax on some flight somewhere that is not refunded if you cancel, hence why AA has to include that language. But in my 20+ years of booking (and canceling) award tickets I've never seen it. It could also just be a relic of the past, for example back when AA charged 'expedite' fees for booking awards within certain times these were always nonrefundable if you canceled.