I fairly certain it isn't available anytime as there are gates around the park that you have to pass to get entry into the park with National Trust charging entry

Hi. The last time we went (a few months ago) the parking at the main site was free for everyone. There are no means to pay and no ticket machines there. BUT at the Studely Royal Site the parking is Pay and Display. (Student Royal is adjacent and connected to the Fountains Abbey site so there really isn’t any need to park there unless your mobility is limited). Hope this helps and that they haven’t changed it by the time you visit.

Yes

As others have said, yes but must be kept on a lead and poop scooped.

parking is free at the visitors centre but there is a charge at the studley royal car park

unlike NT anywhere else it is indeed free

By the West Gate. Don’t use the main one it’s a a very steep route down.

As far I know the Deer Park is part of Fountains Abbey NT estate so you have already booked it when you booked to visit the Abbey, so no you wouldn’t need to book it separately. I doubt people would want to drive over just to view the deers in their own. You do need to drive from Fountains Abbey to the deer park car park as it’s quite a distance.

Hi there, if you think that you'll be visiting several National Trust sites there's the option of buying a membership (which would then give you free parking and access to all National Trust sites as well as your entry to Fountains Abbey on the day). If you ask at our admissions desk they will be able to tell you more about it.

Yes but not in certain areas but plenty of room out side - check their web site though