Yes, there is a nice parkand picnic area.
Yes they are. You do have to pick up after them of course
Mercer was an avid dog lover and had dogs in his castle (Rollo). However dogs are only allowed outside of the castle.
I suspect you are permitted to walk them in the grounds since it is a park (being mindful to pick up after), but I didn't find anything on their site saying one way or the other. I'm certain they will not be permitted in the building itself.
On the grounds maybe, in the building probably not. It should probably be best to call.
What is entry fee
On the grounds absolutely. In the house no
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