As a resident I can tell you there is just about parking for 2 or 3 cars as others replies have suggested. Recently (lockdown lifting in May 202) lots of cars have been left dangerously on the main road. Such cars are starting to be towed. If you plan to visit this lovely viaduct, surrounding countryside and the walks then park further away and make this is highlight of the walk mid way around!

As it is a crop field dogs should be kept to the footpath

There is a foot path that runs right through the viaduct. Moving away from the footpath may be tricky - sometimes physically so as you move along the viaduct due to the structure getting harder to climb into and marshy ground. I have sometimes walked round the field at the back to get a good view square on, and never experienced difficulties. The view from the (public) road is also good.

Not easy... you would really need a taxi out there. It is actually closer to Balcombe station, and if you are keen walkers you could work out a good route from there that took in the viaduct.

I think not. The land is not public, although there is a footpath across it. And a fire at the bridge itself would be regarded as a serious offence.

There's a footpath that passes under the northern end running from the minor road along side. About a 200 yards walk from the road. Tredge.