I'd have no issue with being asked 'what tasks does your dog do'.
The ADA in america allows for this, but the EA doesn't in the UK.
I would not be happy demonstrating my dogs training to someone who hasn't a clue about dogs, my particular conditions, or dog training. My dog is not a circus animal and some of his tasks he can only do in response to my health/behaviour, they're not 'cued' by a word/hand signal. Nor would I be particularly happy discussing my personal health details with a stranger.
Imagine if you could be asked 'why do you need a wheelchair' on entering a store or restaurant? That would be inappropriate!
I do think the information on what an assistance dog may do, what to expect and equally, what isn't appropriate, should be provided to businesses though.
It is appropriate to ask a dog/handler team to leave if the dog is out of control. I also think it would be appropriate if the dog was dripping with mud or the handler was allowing them to leave trails of drool everywhere (take a bloody cloth or don't have a breed that does this).
However, many businesses/staff don't know what certain tasks look like - my friends dog alerts her to passing out by blocking her from moving toward danger (roads for example) and if she ignores, by barking. Many people would see a dog barking at a handler and think the dog is out of control, rather than realise they are actively tasking.
Some dogs may need to actively ignore or almost argue with their handlers at times if they know something the handler doesn't - for example, my dog will indicate a BG drop by shoving his head in my lap but if I am not paying attention, he will absolutely put his paws in my lap and near on ram his face down my throat (very hard to ignore). I went for this indication as I prefer it to be barked at, but to a by-stander it may look like my dog is begging or just climbing on me!
I don't agree with our law that states a dog need not wear any identifying equipment. Sometimes it may be too hot for a vest or it may impede a dog from doing certain tasks, but a marked collar and lead sleeve affect nothing!
I also don't agree with dogs working off lead really, I get that in some cases the dog may need to work off lead - for example, a handler who may collapse or fit, could get a lead wrapped around their neck, or hurt the dog with it, but this is highly unlikely if you're simply holding the lead in your hand. Chances are, you'd drop it! I also don't like dogs taught to leave the handler and find help, the situations where that would be necessary are rare, the chances of the dog just looking like they're lost, being stolen, getting into an accident, are pretty high. If you need that level of care, you need a human carer!