My bike currently lives standing on its back wheel, tucked into a corner. Having just got a new warranty Reverb, is this likely to do it any harm? Same question for the brakes, I guess.

Not in my experience of vertically storing reverb’d bikes for the last 4 years. Shimano brakes seem to need ‘pumping up’ at the lever before riding, but I don’t think that’s unique to vertically stored bikes!