New Zealand Law
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If this is a public place, then you are free to undertake the filming. The same applies for the advertisements which you may or may not have included. If someone places these in a public place, and you decide to film in that area, then there is no problem with copyright. You are quite safe to use the footage
Yes, because the public are free to enter and leave without restriction
You are paying to use the train and not the station.
You can get help from the Privacy Commission website which has guidelines which while not directly on point, will provide some help. Principle 1 of the Privacy Act states that an agency must not collect personal information unless it is for a lawful purpose connected with a function or activity of the agency. The collection must also be necessary for that purpose. So filming in a public place does not offend against privacy, because it is a lawful purpose to make advertisements as part of your job.