Clearly, if the answer to the first question, ‘is the animal trained to provide a service,' is ‘No,' then they are not a service animal and the second question is irrelevant. At this point, you can take your stance to refuse the animal entry if you so choose and likely lose the business, likely get a bad review online, and potentially face legal action.
The second question is irrelevant as it just further complicates things and gets rather personal and awkward if pushed too far. This again is likely to help build the case for the guest to claim they are being discriminated against.
Many people avoid the two questions altogether given that someone could claim they are being discriminated against if not handled properly. When we would ask our guests, what service is the animal trained to provide, we would receive a myriad of different answers ranging from emotional support animals to the pet can sense if I'm about to have a seizure. As you can see, with this second response in particular I am now in this gray area discussing a guest's epilepsy. This guest could claim I didn't allow them to stay because they are epileptic.