No, unless you are visiting as a group. However, you can show up alone and book in person.
The grounds are mixed in terrain and there are some steps externally, there is also some gravel which may not make it ideal for wheelchairs. However, some parts of the grounds are fairly accessible for those using wheelchairs. Internally, there are large, shallow but long staircases to the first floor. However, there is no lift, but the café has information about what you can find upstairs.
Opening times can be found on their website as they can change.
It isn't. You can find out admission costs on their website.