1. Dear Mr. Newbitt, I regret to say that you are responsible for ensuring rainwater from your premises does not run off into a neighbour's property and cause a nuisance. You have to ensure that, for example, the rainwater runoff from your roof, goes into your gutters and that any downpipe from your roof goes into whatever storm drain is available.
2. Under the law laid down in Leakey v. National Trust an occupier of land is liable for all natural as well as non-natural substances egressing from his land if they cause a nuisance to his neighbour. Accordingly, if your rainwater causes a nuisance to your neighbour, you are liable for it and can be sued in damages.
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4. Yes, you are responsible for preventing run off from your driveway to your neighbour driveway which is lower than yours. As I mentioned in my earlier answer, you are responsible for all naturally occurring emissions, such as rainwater which leave your land and which might cause a nuisance to your neighbour. So, you should channel the run off from your driveway into a channel which takes it away from your neighbour's land and instead which goes into a storm drain.