I had a woman recently asked me SO many questions before booking, and the more she asked the more nervous I got, and I decided to decline her request. She was complaining before she was even booking. I have two dogs and the guests have a separate entrance, but she still was nervous. She said her mother was absolutely terrified of dogs. Then she asked if she would ever hear them barking. I have in my notes that yes you do hear them occasionally. She asked about the safety in the neighborhood about the safety walking to the train and would anybody else be around and the more questions she asked the more concerned I was that her expectations about everything, ( even if it was just the dogs barking) - she would downgrade me because of it. So, I politely declined saying that because of the fear of dogs and not having on site parking. I thought she would be better suited to another place ( that had no pets)and I even recommended another one nearby. She was upset by my refusal but I believe that because alarm bells were going off already, I made the right decision.
You were right to decline, but was this an inquiry or a request? You don’t need to decline an inquiry, all you need to do is answer.
It was a request. I do not know where she ended up booking. I really think she needed a hotel, with breakfast, security, parking, etc.
Sounds more like she needs to stay home. 
You followed your gut instints and made the right decision. She sounds very needy and it’s not worth the aggravation.
Yes, definitely the right decision. No host can ever truly guarantee that dogs won’t bark or that any other noises beyond the host’s control won’t happen.
Although our place is very, very quiet, I was asked by a potential guest if I would guarantee that quiet. (I don’t remember why - he needed quiet for working or for catching up on sleep or something).
I told him that although I can say that the place is quiet 99% of the time I can’t be responsible for the neighbours’ gardeners making a noise with their machinery, or a loud boat going by, or the city unexpectedly digging up the road.
For new hosts reading this though, it’s important to remember that not everyone asking a lot of questions will be a troublesome guest.
I remember one man who booked a year or so in advance and contacted me every few days in the year before his stay with what to me were pretty bizarre questions.
I recall that he even wanted to know the height of the bathtub.
When he and his wife stayed here they were model guests. Didn’t bother me with questions once, gave a five-star review and are now regular repeat guests.
So although the OP’s potential guest sounded pretty needy, questions don’t all equate to poor guests. 
I would much rather a guest asked questions to ensure the listing would be a good fit for them, than guests who make assumptions and then complain.
As far as quiet goes, anyone who expects a guarantee of quiet, unless they are booking a remote place with no neighbors and no busy roads anywhere nearby, or one of those castles perched on a mountaintop in Outer Mongolia, has unreasonable ideas.
We’re perched on a hilltop in a tropical rainforest just over a mile from the nearest town and with only one neighbor within 300 yards. I won’t guarantee quiet -the tree frogs can be noisy, party boats can go by, the neighbors can play loud music, etc.
We have exactly the same here. The party boats I can cope with because they don’t happen after early evening but those blasted tree frogs wake me in the early hours. I can (and have) sleep through a hurricane but not those tree frogs!
You were right to decline. Questions like that show a fearful, negative person who will probably complain. I don’t even think they do it maliciously, or out of spite. I think they just lack awareness. I always suggest a hotel when they go on like that.
I just say that my property wouldn’t be a good fit and they’d probably be more comfortable elsewhere.
If I’m uncomfortable about them, I always decline and don’t have any further conversation.
That just says it all there. People are becoming more demanding and entitled, imo. That may be a statement on society, in general, but certainly have come across a lot of utter garbage can humans as an Airbnb host.
Also, the most demanding are always the worst reviewers, or the people who have no respect for house rules, show that they have no respect for all your hard work either.
Airbnb should do more to remove bad actors from the platform. Seems like they will allow almost anything and the hosts bear the burden (and risk), of everything.
I don’t see that Airbnb should do more to remove poor-quality guests, mainly because I don’t understand exactly what they could do.
Many hosts (if this forum over the last eight years is anything to go by) don’t write honest reviews about poor guests or they don’t bother reviewing them at all.
But even if a guest gets a couple of less-than-great reviews, Airbnb still has no way of knowing whether the host was overly picky or that there isn’t some ‘revenge’ reason for the poor review.
Airbnb is there for us to advertise our rentals, to manage credit card payments and other aspects of booking, not to spend time and money determining who can and can’t be good enough to use their platform.
It’s up to us to run our businesses properly, not Airbnb.
I blocked the dates in my calendar one time, so a prospectively complicated booking couldn’t be made. I think i got the idea on this site,
I think you made the right decision for you. We all have a personal list of red flags that tell us if a guest is a good fit for your house (and also your style of management).
You were definitely right in declining. She sounded nothing but trouble.